Subjects -> PHYSICS (Total: 857 journals)
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    - PHYSICS (625 journals)
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    - THERMODYNAMICS (30 journals)

PHYSICS (625 journals)            First | 1 2 3 4 | Last

Showing 201 - 400 of 741 Journals sorted alphabetically
International Journal of Astronomy and Astrophysics     Open Access   (Followers: 37)
International Journal of Biological, Physical and Chemical Studies     Open Access  
International Journal of Computational Materials Science and Surface Engineering     Hybrid Journal   (Followers: 7)
International Journal of Damage Mechanics     Hybrid Journal   (Followers: 5)
International Journal of Engineering and Applied Physics     Open Access  
International Journal of Fatigue     Hybrid Journal   (Followers: 41)
International Journal of Fracture     Hybrid Journal   (Followers: 14)
International Journal of Geometric Methods in Modern Physics     Hybrid Journal   (Followers: 2)
International Journal of Geophysics     Open Access   (Followers: 5)
International Journal of Heat and Fluid Flow     Hybrid Journal   (Followers: 43)
International Journal of Low Radiation     Hybrid Journal  
International Journal of Low-Carbon Technologies     Open Access   (Followers: 1)
International Journal of Mass Spectrometry     Hybrid Journal   (Followers: 16)
International Journal of Material Forming     Hybrid Journal   (Followers: 1)
International Journal of Materials and Product Technology     Hybrid Journal   (Followers: 2)
International Journal of Mechanical Sciences     Hybrid Journal   (Followers: 15)
International Journal of Mechanics and Materials in Design     Hybrid Journal   (Followers: 7)
International Journal of Medical Physics, Clinical Engineering and Radiation Oncology     Open Access   (Followers: 11)
International Journal of Microstructure and Materials Properties     Hybrid Journal   (Followers: 7)
International Journal of Microwave Science and Technology     Open Access   (Followers: 12)
International Journal of Modeling, Simulation, and Scientific Computing     Hybrid Journal   (Followers: 3)
International Journal of Modern Physics A     Hybrid Journal   (Followers: 15)
International Journal of Modern Physics B     Hybrid Journal   (Followers: 12)
International Journal of Modern Physics C     Hybrid Journal   (Followers: 14)
International Journal of Modern Physics D     Hybrid Journal   (Followers: 13)
International Journal of Modern Physics E     Hybrid Journal   (Followers: 13)
International Journal of Multiphysics     Open Access  
International Journal of Nanomanufacturing     Hybrid Journal  
International Journal of Nanoscience     Hybrid Journal  
International Journal of Nanotechnology     Hybrid Journal   (Followers: 9)
International Journal of Non-Linear Mechanics     Hybrid Journal   (Followers: 8)
International Journal of Nonlinear Dynamics and Control     Hybrid Journal   (Followers: 6)
International Journal of Physics     Open Access   (Followers: 10)
International Journal of PIXE     Hybrid Journal  
International Journal of Plasticity     Hybrid Journal   (Followers: 7)
International Journal of Quantum Information     Hybrid Journal   (Followers: 6)
International Journal of Self-Propagating High-Temperature Synthesis     Hybrid Journal  
International Journal of Solids and Structures     Hybrid Journal   (Followers: 14)
International Journal of Surface Science and Engineering     Hybrid Journal   (Followers: 6)
International Journal of Theoretical and Applied Multiscale Mechanics     Hybrid Journal   (Followers: 3)
International Journal of Theoretical and Mathematical Physics     Open Access   (Followers: 13)
International Journal of Theoretical Physics     Hybrid Journal   (Followers: 17)
International Journal of Thermal Sciences     Hybrid Journal   (Followers: 19)
International Journal on Smart Sensing and Intelligent Systems     Open Access  
International Letters of Chemistry, Physics and Astronomy     Open Access   (Followers: 9)
International Materials Reviews     Hybrid Journal   (Followers: 15)
Iranian Journal of Medical Physics     Open Access  
Iranian Journal of Science and Technology, Transactions A : Science     Hybrid Journal  
Ironmaking & Steelmaking     Hybrid Journal   (Followers: 4)
Izvestiya, Atmospheric and Oceanic Physics     Full-text available via subscription   (Followers: 1)
Izvestiya, Physics of the Solid Earth     Hybrid Journal   (Followers: 2)
Jambura Physics Journal     Open Access  
JETP Letters     Hybrid Journal   (Followers: 3)
Journal of Adhesion Science and Technology     Hybrid Journal   (Followers: 10)
Journal of Advanced Physics     Full-text available via subscription   (Followers: 13)
Journal of Advances in Physics     Open Access   (Followers: 13)
Journal of Applied Mathematics and Physics     Open Access   (Followers: 9)
Journal of Applied Mechanics and Technical Physics     Hybrid Journal   (Followers: 7)
Journal of Applied Physics     Hybrid Journal   (Followers: 69)
Journal of Applied Spectroscopy     Hybrid Journal   (Followers: 9)
Journal of Astrophysics     Open Access   (Followers: 34)
Journal of Astrophysics and Astronomy     Open Access   (Followers: 59)
Journal of Building Physics     Hybrid Journal   (Followers: 1)
Journal of Chromatographic Science     Hybrid Journal   (Followers: 15)
Journal of Complex Networks     Hybrid Journal   (Followers: 1)
Journal of Composite Materials     Hybrid Journal   (Followers: 250)
Journal of Computational and Theoretical Transport     Hybrid Journal   (Followers: 2)
Journal of Computational Methods in Physics     Open Access   (Followers: 8)
Journal of Computational Physics     Hybrid Journal   (Followers: 60)
Journal of Computational Physics : X     Open Access   (Followers: 1)
Journal of Contemporary Physics (Armenian Academy of Sciences)     Hybrid Journal   (Followers: 9)
Journal of Dynamic Systems, Measurement, and Control     Full-text available via subscription   (Followers: 14)
Journal of Elasticity     Hybrid Journal   (Followers: 7)
Journal of Electron Spectroscopy and Related Phenomena     Hybrid Journal   (Followers: 3)
Journal of Electronic Materials     Hybrid Journal   (Followers: 3)
Journal of Electronics Cooling and Thermal Control     Open Access   (Followers: 9)
Journal of Engineering Materials and Technology     Full-text available via subscription   (Followers: 17)
Journal of Engineering Physics and Thermophysics     Hybrid Journal   (Followers: 2)
Journal of Experimental and Theoretical Physics     Hybrid Journal   (Followers: 4)
Journal of Experimental Physics     Open Access   (Followers: 3)
Journal of Fire Sciences     Hybrid Journal   (Followers: 6)
Journal of Geometry and Physics     Full-text available via subscription   (Followers: 2)
Journal of Geophysical Research : Space Physics     Full-text available via subscription   (Followers: 144)
Journal of Gravity     Open Access   (Followers: 4)
Journal of High Energy Astrophysics     Full-text available via subscription   (Followers: 26)
Journal of High Energy Physics     Hybrid Journal   (Followers: 17)
Journal of High Energy Physics, Gravitation and Cosmology     Open Access   (Followers: 2)
Journal of Hydrogels     Full-text available via subscription  
Journal of Hyperspectral Remote Sensing     Open Access   (Followers: 23)
Journal of Imaging     Open Access   (Followers: 3)
Journal of Information Display     Open Access   (Followers: 1)
Journal of Intelligent Material Systems and Structures     Hybrid Journal   (Followers: 8)
Journal of Lightwave Technology     Hybrid Journal   (Followers: 14)
Journal of Low Frequency Noise, Vibration and Active Control     Open Access   (Followers: 8)
Journal of Luminescence     Hybrid Journal   (Followers: 2)
Journal of Materials Engineering and Performance     Hybrid Journal   (Followers: 22)
Journal of Materials Physics and Chemistry     Open Access   (Followers: 7)
Journal of Materials Science     Hybrid Journal   (Followers: 26)
Journal of Materials Science : Materials in Electronics     Hybrid Journal   (Followers: 2)
Journal of Materials Science : Materials in Medicine     Hybrid Journal   (Followers: 1)
Journal of Mathematical Fluid Mechanics     Hybrid Journal   (Followers: 10)
Journal of Mathematical Physics     Hybrid Journal   (Followers: 25)
Journal of Medical Imaging and Health Informatics     Full-text available via subscription  
Journal of Medical Ultrasonics     Hybrid Journal   (Followers: 2)
Journal of Micro/Nanolithography MEMS and MOEMS     Hybrid Journal   (Followers: 24)
Journal of Molecular Spectroscopy     Hybrid Journal   (Followers: 6)
Journal of Motor Behavior     Hybrid Journal   (Followers: 8)
Journal of Multiscale Modeling     Hybrid Journal   (Followers: 1)
Journal of Nepal Physical Society     Open Access  
Journal of Nondestructive Evaluation     Hybrid Journal   (Followers: 11)
Journal of Nonlinear Dynamics     Open Access   (Followers: 6)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 2)
Journal of Nuclear Physics, Material Sciences, Radiation and Applications     Open Access   (Followers: 6)
Journal of Optics     Hybrid Journal   (Followers: 17)
Journal of Photonics for Energy     Hybrid Journal   (Followers: 2)
Journal of Physical and Chemical Reference Data     Hybrid Journal   (Followers: 4)
Journal of Physical Chemistry B     Hybrid Journal   (Followers: 48)
Journal of Physical Chemistry C     Hybrid Journal   (Followers: 36)
Journal of Physical Oceanography     Hybrid Journal   (Followers: 19, SJR: 2.461, CiteScore: 3)
Journal of Physical Organic Chemistry     Hybrid Journal   (Followers: 8)
Journal of Physics and Chemistry of Solids     Hybrid Journal   (Followers: 3)
Journal of Plasma Physics     Hybrid Journal   (Followers: 21)
Journal of Polymer Science Part B: Polymer Physics     Hybrid Journal   (Followers: 22)
Journal of Porous Materials     Hybrid Journal   (Followers: 4)
Journal of Porphyrins and Phthalocyanines     Hybrid Journal   (Followers: 1)
Journal of Quantitative Spectroscopy and Radiative Transfer     Hybrid Journal   (Followers: 3)
Journal of Reinforced Plastics and Composites     Hybrid Journal   (Followers: 30)
Journal of Rheology     Full-text available via subscription   (Followers: 7)
Journal of Sandwich Structures and Materials     Hybrid Journal   (Followers: 4)
Journal of Scientific Research     Open Access  
Journal of Sensors     Open Access   (Followers: 25)
Journal of Sol-Gel Science and Technology     Hybrid Journal  
Journal of Solid State Physics     Open Access   (Followers: 8)
Journal of Spectroscopy     Open Access   (Followers: 6)
Journal of Superconductivity and Novel Magnetism     Partially Free   (Followers: 1)
Journal of Synchrotron Radiation     Open Access   (Followers: 3)
Journal of the American Society for Mass Spectrometry     Hybrid Journal   (Followers: 31)
Journal of the ICRU     Hybrid Journal  
Journal of the Korean Physical Society     Partially Free  
Journal of the Physical Society of Japan     Hybrid Journal   (Followers: 2)
Journal of Theoretical and Applied Physics     Open Access   (Followers: 9)
Journal of Tissue Engineering     Open Access   (Followers: 6)
Journal of Ultrasound in Medicine     Full-text available via subscription   (Followers: 11)
Journal of Vibration and Control     Hybrid Journal   (Followers: 43)
Journal of Visualization     Hybrid Journal   (Followers: 3)
Journal of Zhejiang University : Sceince A     Hybrid Journal  
JPSE (Journal of Physical Science and Engineering)     Open Access  
Jurnal Fisika     Open Access  
Jurnal Ilmiah Pendidikan Fisika Al-Biruni     Open Access  
Jurnal NEUTRINO     Open Access  
Jurnal Online of Physics     Open Access  
Jurnal Pendidikan Fisika Indonesia (Indonesian Journal of Physics Education)     Open Access  
Jurnal Penelitian Fisika dan Aplikasinya     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Karbala International Journal of Modern Science     Open Access  
Kasuari : Physics Education Journal     Open Access  
La Rivista del Nuovo Cimento     Hybrid Journal  
Lasers in Surgery and Medicine     Hybrid Journal   (Followers: 1)
Latvian Journal of Physics and Technical Sciences     Open Access  
Letters in High Energy Physics     Open Access  
Letters in Mathematical Physics     Hybrid Journal   (Followers: 4)
Light : Science & Applications     Open Access   (Followers: 3)
Living Reviews in Computational Astrophysics     Open Access   (Followers: 3)
Living Reviews in Relativity     Open Access  
Living Reviews in Solar Physics     Open Access   (Followers: 1)
Lubrication Science     Hybrid Journal   (Followers: 2)
Macalester Journal of Physics and Astronomy     Open Access   (Followers: 6)
Machining Science and Technology: An International Journal     Hybrid Journal   (Followers: 2)
Magnetic Resonance     Open Access  
Magnetic Resonance Letters     Open Access  
Magnetic Resonance Materials in Physics, Biology and Medicine     Hybrid Journal   (Followers: 3)
MAPAN     Hybrid Journal  
Mass Spectrometry Reviews     Hybrid Journal   (Followers: 30)
Matéria (Rio de Janeiro)     Open Access  
Materials and Design     Open Access   (Followers: 47)
Materials at High Temperatures     Full-text available via subscription   (Followers: 3)
Materials Chemistry and Physics     Full-text available via subscription   (Followers: 15)
Materials Research Bulletin     Hybrid Journal   (Followers: 25)
Materials Research Innovations     Hybrid Journal   (Followers: 1)
Materials Science     Hybrid Journal   (Followers: 8)
Materials Science and Engineering: A     Hybrid Journal   (Followers: 44)
Materials Science and Engineering: B     Hybrid Journal   (Followers: 22)
Materials Science and Engineering: R: Reports     Hybrid Journal   (Followers: 15)
Materials Science and Technology     Hybrid Journal   (Followers: 40)
Materials Today Physics     Hybrid Journal   (Followers: 1)
Matériaux & Techniques     Full-text available via subscription   (Followers: 2)
Mathematical Physics, Analysis and Geometry     Hybrid Journal   (Followers: 3)
Mathematics and Mechanics of Solids     Hybrid Journal   (Followers: 3)
Matter and Radiation at Extremes     Open Access   (Followers: 1)
Meccanica     Hybrid Journal   (Followers: 1)
Mechanics of Advanced Materials and Structures     Hybrid Journal   (Followers: 6)
Mechanics of Materials     Hybrid Journal   (Followers: 25)
Mechanics of Time-Dependent Materials     Hybrid Journal   (Followers: 2)
Mechanics Research Communications     Hybrid Journal   (Followers: 4)
Medical Physics     Hybrid Journal   (Followers: 17)
Micro and Nano Systems Letters     Open Access   (Followers: 6)
Microfluidics and Nanofluidics     Hybrid Journal   (Followers: 11)
Microporous and Mesoporous Materials     Hybrid Journal   (Followers: 9)
Modern Instrumentation     Open Access   (Followers: 57)
Modern Physics Letters A     Hybrid Journal   (Followers: 14)

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Similar Journals
Journal Cover
Mathematics and Mechanics of Solids
Journal Prestige (SJR): 0.768
Citation Impact (citeScore): 2
Number of Followers: 3  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1081-2865 - ISSN (Online) 1741-3028
Published by Sage Publications Homepage  [1174 journals]
  • Reflection and refraction of plane wave at the junction of two dissimilar
           pre-stressed functionally graded piezothermoelastic media under different
           interfacial conditions

    • Free pre-print version: Loading...

      Authors: Subhashis Karmakar, Sanjeev Anand Sahu, Suman Goyal
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The present paper deals with the study of the reflection and refraction of plane waves (quasi P wave, quasi SV wave, electroacoustic wave, and thermal wave) at the common interface of two dissimilar initially stressed functionally graded piezothermoelastic media. The problem has been formulated and solved using suitable boundary conditions, and the results are obtained in a closed matrix form. The effect of mechanical, electrical, and thermal loose bonding of the common interface on the reflection and refraction coefficients are analyzed and theoretical outcomes are presented through graphs under two generalized forms of thermoelasticity (namely, Lord and Shulman (LS) theory, Green and Lindsay (GL) theory). A particular model of CdSe and PZT-5A materials has been considered for the numerical illustration. Moreover, the effect of material gradient; horizontal, transverse, and normal initial stresses; thermal relaxation parameters; and material coefficients on the reflection and refraction coefficients are demonstrated with the help of graphs. The expressions for energy ratios of reflected and refracted waves are derived, and energy conservation is validated with the help of obtained graphs under LS and GL theories. The study finds its application toward the efficient optimization of force sensors, surface acoustic wave (SAW) devices, temperature sensors, and Love wave sensors.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-20T11:55:48Z
      DOI: 10.1177/10812865221099502
       
  • Continuum mechanics versus the mathematical analysis of its differential
           equations: In Memoriam Tony Spencer

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      Authors: Stuart S Antman
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In 1966, A. J. M. Spencer gave an inaugural lecture on continuum mechanics on the occasion of his appointment to a professorship at the University of Nottingham. The lecture gave an accurate, but nontechnical, picture of the interaction of mathematics and continuum mechanics at that time, together with a prediction of their subsequent hoped-for interactions. This article responds to Spencer’s lecture by surveying these fields as of 1966, by tracing their developments, interactions, and lack thereof in the subsequent years, and by commenting on the prospects for the future.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-20T11:51:23Z
      DOI: 10.1177/10812865221095292
       
  • An experimental study of morphological formation in bilayered tubular
           structures driven by swelling/growth

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      Authors: Rui-Cheng Liu, Lishuai Jin, Zongxi Cai, Yang Liu
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Circumferential wrinkling in soft tubular tissues is vital in supporting normal physiological functions. Most existing literature was dedicated to theoretical modeling and finite element simulations based on a specific growth model. This paper presents an experimental investigation on pattern formation and evolution in bilayered tubular organs using swelling deformation of polydimethylsiloxane (PDMS) and aims at supplying a thorough comparison with theoretical and finite element results. To create a twin model in modeling and simulation, the shear modulus in the incompressible neo-Hookean material is estimated via uni-axial tensile and pure shear tests. Five bilayered tubes with different material or geometrical parameters are fabricated. Swelling experiments are carried out for these samples in an individual experimental setup where a plane-strain deformation is guaranteed, and several surface patterns and the associated mode transformations are observed, namely, creases, wrinkles, period-doubling profiles, wrinkle-to-crease transition, and wrinkle-to-period-doubling transition. In particular, an interfacial wrinkling pattern is also observed. To make comparisons, a buckling analysis is conducted within the framework of finite elasticity by means of the Stroh formulation and a refined surface impedance matrix method. In addition, a finite element analysis (FEA) is performed to trace the evolution of surface instabilities. It turns out that the experimental findings agree well with the theoretical predictions as well as the finite element results. From our experiments, it is found that creasing mode may appear instead of wrinkling mode when both layers share a similar mechanical property. It is expected that the current work could provide novel experimental insight into pattern formation in tubular structures. In particular, the traditional impedance matrix method has been adapted, which enables us to resolve eigenvalue problems with displacement boundary conditions, and the good agreement among experimental, theoretical, and simulation consequences supplies strong evidence that a phenomenological growth model is satisfactory to reveal mechanisms behind intricate surface morphology in tubular tissues.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-17T12:35:55Z
      DOI: 10.1177/10812865221099204
       
  • Lattice infill structure design of topology optimization considering size
           effect

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      Authors: Tian Li, Bo Sun, Ning Gan
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The vigorous development of additive manufacturing technology promotes the tendency of lattice infill design to be miniaturized. The representative scale of the deformation field becomes equivalent to the length scale of the microstructures when the characteristics size of the lattice infill design is down to micron or nanoscale, and strain gradient effects or size effects arise in the structure. Due to the lack of microscopic material properties, the typical topology optimization framework based on classical mechanics for lattice infill structure cannot represent the performance difference induced by the size effect. Therefore, single-scale lattice infill structure design and couple stress theory are combined to explore the size effect on topology optimization. Numerical examples show that when the size ratio of the macroscopic feature size to the material characteristic length is reduced to a comparable range, the topological configurations and the target compliance values exhibit a significant size effect.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-16T10:58:43Z
      DOI: 10.1177/10812865221103291
       
  • The analysis and computation on nonlocal thermoelastic problems of blend
           composites via enriched second-order multi-scale computational method

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      Authors: Hao Dong, Yufeng Nie, Ruyun Ma, Yaochuang Han
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      This paper proposes an innovative enriched second-order multi-scale (SOMS) computational method to simulate and analyze the nonlocal thermoelastic problems of blend composites with stress and heat flux gradient behaviors. The multiple periodical heterogeneities and periodic configurations of investigated blend composites in different substructures result in a huge computational cost for direct numerical simulations. The significant characteristics of this study are as follows. (1) The nonlocal properties of blend composites in constitutive equations are converted into the source terms of thermoelastic balance equations. The novel macro-micro coupled SOMS computational model for these transformed nonlocal multi-scale problems is derived on the basis of multi-scale asymptotic analysis. The nonlocal thermoelastic behaviors of blend composites can be merely uncovered in the enriched SOMS solutions. (2) The error analysis in the pointwise sense is presented to elucidate the importance and necessity of establishing the enriched SOMS solutions. Furthermore, an explicit error estimate for the SOMS approximate solutions is obtained in the integral sense for these nonlocal multi-scale problems. (3) A multi-scale numerical algorithm is presented to effectively simulate nonlocal thermoelastic problems of blend composites based on finite element method (FEM). Finally, the capability of the proposed enriched SOMS computational method is demonstrated by typical two-dimensional (2D) and three-dimensional (3D) blend composites, presenting not only the excellent numerical accuracy but also the less computational cost. This work proposes a unified multi-scale computational framework for enabling nonlocal thermoelastic behavior analysis of blend composites.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-13T10:23:30Z
      DOI: 10.1177/10812865221098352
       
  • Vibrations in finitely deformed residual stressed circular cylindrical
           tubes

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      Authors: Anas Kanan, Michael Kaliske, Luis Dorfmann
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A residually stressed thick-walled tube is subject to a combination of internal or external pressure and axial stretch to maintain its circular cylindrical geometry. A small incremental motion is then superimposed on the finitely deformed configuration. We summarize the basic elements of the theory of hyperelasticity with initial stress, together with the corresponding incremental forms. Equations are derived and used to evaluate the dependence of the axial load, of the vibration frequency and of the circumferential stress, on the inner and outer curved boundaries, on the residual stress and on various geometric quantities. The theory is applied to a simple neo-Hookean model with two material parameters and a parameter to scale the magnitude of the residual stress. The static response to small incremental deformations is obtained as a special case when the vibration frequency vanishes.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-13T10:20:53Z
      DOI: 10.1177/10812865221098185
       
  • Internal resonances of nanorods in presence of surface energy effect:
           Nonlinear torsional vibration

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      Authors: R Nazemnezhad, Reza Mehrianpoor, Ali Akbar Jandaghian
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, effects of the surface energy on the nonlinear torsional vibrations and internal resonances of nanorods are investigated. To this end, the second-order term with respect to angle of rotation is considered for the displacement field. In addition, the geometrically nonlinear strain–displacement relations are obtained based on the von-Kármán theory. Then, Hamilton’s principle is implemented to derive the governing equation of motion for torsional vibration of nanorod. In the governing equation of motion, the surface energy parameters are included by the surface elasticity theory. The multiple-scale method is employed to solve the governing equation of motion for fixed-free and fixed-fixed end conditions. The nanorod considered is made of aluminum and silicon because of different values of their surface parameters. The effect of surface energy parameters on the torsional frequencies of nanorods is investigated for different values of length, radius, frequency number, and amplitude of the nonlinear vibrations. In addition the cases of occurring, the internal resonances are reported. The results obtained in this research may be useful for better design of nanoelectromechanical devices such as nanobearings and rotary servomotors.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-13T01:28:34Z
      DOI: 10.1177/10812865221102326
       
  • On Spencer’s displacement function approach for problems in
           second-order elasticity theory

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      Authors: APS Selvadurai
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The paper describes the displacement function approach first proposed by AJM Spencer for the formulation and solution of problems in second-order elasticity theory. The displacement function approach for the second-order problem results in a single inhomogeneous partial differential equation of the form [math], where [math] is Stokes’ operator and [math] depends only on the first-order or the classical elasticity solution. The second-order isotropic stress [math] is governed by an inhomogeneous partial differential equation of the form [math], where [math] is Laplace’s operator and [math] depends only on the first-order or classical elasticity solution. The introduction of the displacement function enables the evaluation of the second-order displacement field purely through its derivatives and avoids the introduction of arbitrary rigid body terms normally associated with formulations where the strains need to be integrated. In principle, the displacement function approach can be systematically applied to examine higher-order effects, but such formulations entail considerable algebraic manipulations, which can be facilitated through the use of computer-aided symbolic mathematical operations. The paper describes the advances that have been made in the application of Spencer’s fundamental contribution and applies it to the solution of Kelvin’s concentrated force, Love’s doublet, and Boussinesq’s problems in second-order elasticity theory.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-10T10:59:18Z
      DOI: 10.1177/10812865221096771
       
  • Vibrational analysis of harmonic oscillator chains with random topological
           constraints

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      Authors: Uwe Michael Mühlich
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The effect of topological disorder on the dynamic behaviour of topologically constrained oscillator chains is investigated through a normal mode analysis. A measure for mode localization based on the skewness of the density of energy states of normal modes is proposed, which correlates well with main configuration characteristics. Appropriate configuration sampling is achieved by employing the Ising model together with the Metropolis algorithm.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-08T11:05:53Z
      DOI: 10.1177/10812865221101131
       
  • Fiber orientation distributions based on planar fiber orientation tensors
           of fourth order

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      Authors: Julian Karl Bauer, Thomas Böhlke
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Fiber orientation tensors represent averaged measures of fiber orientations inside a microstructure. Although, orientation-dependent material models are commonly used to describe the mechanical properties of representative microstructure, the influence of changing or differing microstructure on the material response is rarely investigated systematically for directional measures which are more precise than second-order fiber orientation tensors. For the special case of planar orientation distributions, a set of admissible fiber orientation tensors of fourth-order is known. Fiber orientation distributions reconstructed from given orientation tensors are of interest both for numerical averaging schemes in material models and visualization of the directional information itself. Focusing on the special case of planar orientations, this paper draws the geometric picture of fiber orientation distribution functions reconstructed from fourth-order fiber orientation tensors. The developed methodology can be adopted to study the dependence of material models on planar fourth-order fiber orientation tensors. Within the set of admissible fiber orientation tensors, a subset of distinct tensors is identified. Advantages and disadvantages of the description of planar orientation states in two- or three-dimensional tensor frameworks are demonstrated. Reconstruction of fiber orientation distributions is performed by truncated Fourier series and additionally by deploying a maximum entropy method. The combination of the set of admissible and distinct fiber orientation tensors and reconstruction methods leads to the variety of reconstructed fiber orientation distributions. This variety is visualized by arrangements of polar plots within the parameter space of fiber orientation tensors. This visualization shows the influence of averaged orientation measures on reconstructed orientation distributions and can be used to study any simulation method or quantity which is defined as a function of planar fourth-order fiber orientation tensors.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-08T10:49:39Z
      DOI: 10.1177/10812865221093958
       
  • The pull-in instability and eigenfrequency variations of a graphene
           resonator under electrostatic loading

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      Authors: Yin Zhang, Ya-pu Zhao
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A continuum membrane model is presented to describe the pull-in instability and eigenfrequency variations of a graphene resonator under an electrostatic loading. The pull-in instability leads to the device failure and the eigenfrequency variation determines its frequency tuning range, which are among the most important aspects in a micro/nanomechanical resonator design. The von Kármán kinematic assumptions are used for the membrane large deflection. The geometric nonlinearity resulting from a large deflection and the physical nonlinearity resulting from an electrostatic loading are the two competing mechanisms: the geometric nonlinearity stiffens the membrane structure and the physical nonlinearity softens it. The effects of these two competing mechanisms together with the initial tensile strain on the pull-in instability and eigenfrequency variations are vividly demonstrated. With the aim of achieving a higher accuracy, a multimodal computation method together with its convergence study and error analysis is also presented.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-08T04:51:45Z
      DOI: 10.1177/10812865221101120
       
  • A novel reduced model for a linearized anisotropic rod with doubly
           symmetric a cross-section: I. Theory

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      Authors: Erick Pruchnicki, Xiaoyi Chen, Hui-Hui Dai
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A novel reduced model is constructed for a linearized anisotropic rod with doubly symmetric cross-section. The derivation starts from the Taylor expansion of the displacement vector and the stress tensor. The goal is to establish rod equations for the leading order displacement and the twist angle of the mean line of the rod in an asymptotically consistent way. Fifteen vector differential equations are derived from the 3D (three-dimensional) governing system, and elaborate manipulations between these equations (including the Fourier series expansion of the lateral traction condition) lead to four scalar rod equations: two bending equations, one twisting equation, and one stretching equation. Also, recursive relations are established between the higher order coefficients and the lower order ones, which eliminate most of the unknowns. Six boundary conditions at each edge are obtained from the 3D virtual work principle, and 1D (one-dimensional) virtual work principle is also developed. The rod model has three features: it adopts no ad hoc assumptions for the displacement form and the scalings of the external loadings; it incorporates the bending, twisting, and stretching effects in one uniform framework; and it satisfies the 3D governing system in a point-wise manner.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-08T04:48:49Z
      DOI: 10.1177/10812865221094507
       
  • Stress concentration due to an elliptic hole in a porous elastic plate

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      Authors: Bhaskar Vajipeyajula, Pavitra Murru, Kumbakonam Ramamani Rajagopal
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We study the state of stress and strain in a square plate containing an elliptic hole in the case of a porous elastic solid undergoing small strain, using a constitutive relation that has been put into place recently to describe the response of such solids undergoing small strains. We carry out the study by solving the problem numerically. We verify that our numerical solutions agree with those for the classical linearized elastic solid when certain appropriate material parameters are set to zero. We show that the stress concentration factor in the case of the porous elastic solid can be much higher, as much as 300% of the stress concentration in the case of the classical linearized elastic solid, when the aspect ratio is sufficiently small, depending on the values of certain material parameters. The difference between the stress concentration for the porous solid increases as the aspect ratio (the ratio of the major axis to the minor axis) decreases. By allowing the aspect ratio of the ellipse to go to zero, we can obtain the state of stress and strain adjacent to a crack in the square plate; however, in this limit, the strains would greatly exceed the assumption under which the constitutive theory is derived.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-06-04T08:23:16Z
      DOI: 10.1177/10812865221097686
       
  • Lagrange formal calculus as applied to Lagrange mechanics: An exercise in
           anachronism

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      Authors: Alberto Maria Bersani, Enrico Bersani, Paolo Caressa
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      When Lagrange wrote his masterpiece Mécanique Analytique, the foundations of analysis were not completely understood: to erect the great building of Analytical Mechanics upon solid foundations, the Piedmontese mathematician tried to lay the foundations of differential calculus in a purely algebraic way, using power series instead of functions, regardless about convergence and uniqueness issues. While this foundation was unsatisfactory as shown by Cauchy some decades later, it can shed light on how Lagrange considered the analytical objects (curves, energies, etc.) he dealt with in Mechanics. In this paper, we review these Lagrangian foundations of analysis, and we try to adopt its obvious modern counterpart, i.e., formal power series, to express some results in Analytical Mechanics related to Helmholtz conditions and Rayleigh description of dissipation. By means of purely algebraic manipulations, we will easily recover results otherwise proved by means of modern analysis.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-21T09:35:41Z
      DOI: 10.1177/10812865221096685
       
  • Statistical prediction of bone microstructure degradation to study patient
           dependency in osteoporosis

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      Authors: Seyedfarzad Famouri, Mostafa Baghani, Azadeh Sheidaei, Daniel George, Maryam Mazraehei Farahani, Masoud Shariat Panahi, Majid Baniassadi
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Numerical prediction of osteoporosis evolution is a challenging objective in medicine, particularly when one desires to account for patient dependency. The use of statistical methods to reconstruct bone microstructure distribution could be a helpful tool for this prediction, as they are able to provide different types of microstructures that can be optimized to fit with each patient. An initial bone sample was obtained from high-resolution X-ray computed tomography (HRmCT). Its microstructure evolution in time using a previously developed degradation model was used as the ground truth. Statistical bone microstructures were reconstructed at different stages of this evolution using two-point correlation functions (TPCFs). A blind search approach is used to find the optimized statistical microstructures, and the optimized coefficient showed less than 2% TPCF error between the statistical reconstruction and the degraded model. The statistical models also showed less than 13% error in the corresponding mechanical properties. The results showed a good correlation between the developed approach and the ground truth. The method could be extrapolated to account for the physical characterization of patient dependency to predict bone density loss over time.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-16T06:15:17Z
      DOI: 10.1177/10812865221098777
       
  • Understanding the role of interfacial mechanics on the wrinkling behavior
           of compressible bilayer structures under large plane deformations

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      Authors: A Derya Bakiler, Ali Javili
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Layered soft structures under loading may buckle in order to release energy. One commonly studied phenomenon is the wrinkling behavior of a bilayer system consisting of a stiff film on top of a compliant substrate, which has been observed ubiquitously in nature and has found several applications. While the wrinkling behavior of the incompressible bilayer system has been explored thoroughly, the large deformation behavior of a compressible bilayer system had been virtually unexplored until very recently. On the contrary, it is well established where more than one material is concerned, there always exists an interphase region between different constituents whose mechanical modeling has presented itself as a long-lasting challenge. To address these gaps in the literature, herein we first propose a theoretical, generic, large deformations framework to capture the instabilities of a compressible domain containing an interface. The general interface model is employed such that at its limits, the elastic and the cohesive interface models are recovered. The instability behavior of a compressible bilayer domain undergoing large deformations for a wide range of cohesive stiffness values, stiffness ratios, compressibilities, and film thicknesses is systematically explored. In particular, it is shown that delamination of the film can also be captured via this interface model. In addition, this generic framework is examined for a coated beam and a coated half-space too. The results of the theoretical framework are thoroughly compared to numerical results obtained via finite element method simulations enhanced with eigenvalue analysis, and an excellent agreement between the two sets of results is observed. It is found that varying substrate Poisson’s ratio has a significant effect on the bifurcation behavior for higher cohesive stiffnesses. Remarkably, while in classical bilayers the critical stretch at wrinkling is independent of the film thickness, herein we discover a significant dependence of the critical stretch to the film thickness in the presence of the interface.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-16T06:12:29Z
      DOI: 10.1177/10812865221094833
       
  • Material swelling with partial confinement in the internally balanced
           generalization of hyperelasticity

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      Authors: Vahid Zamani, Hasan Demirkoparan, Thomas J Pence
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The internally balanced material theory, which can be viewed as a generalization of hyperelasticity, is extended to treat material swelling. Swelling problems involving eventual contact with fixed rigid surfaces are considered, first for a situation where the post-contact deformation is homogeneous, and then for a situation where the post-contact deformation is not homogeneous. The latter requires the solution of a boundary value problem in the internally balanced material setting. Both situations are considered in detail for a neo-Hookean-like constitutive specification in the internally balanced material framework.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-13T10:06:03Z
      DOI: 10.1177/10812865221092377
       
  • Rules governing swarm robot in continuum mechanics

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      Authors: Ramiro dell’Erba
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      To determine material body’s deformation is usual to solve Newton’s equation, under assigned boundary conditions; but this is not the only possibility to obtain a plausible description of the phenomenon. In recent years, position-based dynamic (PBD) concept has consolidated its success. The idea has its roots in computer graphic graphics aimed at saving processing time in computing object’s deformation and breakage in video games applications; PBD tries to give a plausible description of the deformation taking into account only the relative point’s positions to describe the action of internal forces. The aim is to obtain an algebraical equation capable of calculating the position of a point using as input the position of some other points. This kinematic approach has the advantage to work with simple algebraical equations; the complexity of the system increases linearly, rather than quadratically, with increasing the point’s number. Working on swarm robotics we have addressed the problem concerning flocking rules, to determine the behaviour of a single element to achieve an assigned configuration of the group. One possibility to perform this task, for each single robot, is to see what some of its neighbours are doing. We then use these rules to reproduce some behaviour of bi-dimensional deformable bodies both consistent with the standard Cauchy model and according to the second-gradient theory. All constitutive properties of the material are hidden within the rules, determining the displacements of the particles each relative to the others. The tool has an advantage in terms of computational cost and is very flexible to be adapted to objects of complex geometry and problems of different nature. The results are encouraging and fracture can be easily managed. However, a connection between the parameters of the tool and the constitutive parameters of the materials is not yet provided and our efforts are addressed in this direction, to validate the tool by a solid classical theory.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-13T10:02:31Z
      DOI: 10.1177/10812865221088795
       
  • Dynamic amplification in a periodic structure with a transition zone
           subject to a moving load: Three different phenomena

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      Authors: Andrei B Fărăgău, João M de Oliveira Barbosa, Andrei V Metrikine, Karel N van Dalen
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The study of periodic systems under the action of moving loads is of high practical importance in railway, road, and bridge engineering, among others. Even though plenty of studies focus on periodic systems, few of them are dedicated to the influence of a local inhomogeneous region, a so-called transition zone, on the dynamic response. In railway engineering, these transition zones are prone to significant degradation, leading to more maintenance requirements than the rest of the structure. This study aims to identify and investigate phenomena that arise due to the combination of periodicity and local inhomogeneity in a system acted upon by a moving load. To study such phenomena in their purest form, a one-dimensional model is formulated consisting of a constant moving load acting on an infinite string periodically supported by discrete springs and dashpots, with a finite domain in which the stiffness and damping of the supports is larger than for the rest of the infinite domain; this model is representative of a catenary system (overhead wires in railway tracks). The identified phenomena can be considered as additional constraints for the design parameters at transition zones such that dynamic amplifications are avoided.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-11T06:29:13Z
      DOI: 10.1177/10812865221094318
       
  • A slender body theory for the motion of special Cosserat filaments in
           Stokes flow

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      Authors: Mohit Garg, Ajeet Kumar
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The motion of filament-like structures in fluid media has been a topic of interest since long. In this regard, a well known slender body theory exists, wherein the fluid flow is assumed to be Stokesian while the filament is modeled as a Kirchhoff rod which can bend and twist but remains inextensible and unshearable. In this work, we relax the inextensibility and unshearability constraints on filaments, i.e., the filament is modeled as a special Cosserat rod. Starting with the boundary integral formulation of Stokes flow involving the filament’s surface velocity and fluid traction that acts on the filament surface, the method of matched asymptotic expansion is used to first obtain a leading-order representation of the boundary integral kernels in the filament’s aspect ratio. We then substitute Fourier series expansion (in filament’s circumferential coordinate) of both the filament’s surface velocity and fluid traction in the aforementioned leading-order representation and further linearize it in the rod’s shear strains to reduce the two-dimensional boundary integral over the filament surface into a line integral over the filament’s centerline. Upon further collecting the coefficients of sine and cosine terms, the zeroth-order Fourier mode yields a line integral equation relating the rod’s centerline velocity with the distributed fluid force that acts on the filament. The presence of line integral makes the relation non-local in nature. On the contrary, the first-order Fourier mode yields a simpler local relation between the rod’s angular velocity and the distributed fluid couple. The line integral equation is shown to reduce to the classical slender body theory when shear strains and axial strain are set to zero. The non-dimensional governing equations of the special Cosserat rod are also derived accounting for the distributed fluid force and distributed fluid couple in them which are solved to obtain the filament motion. The presented theory is demonstrated with an example problem of the tumbling of filaments in background shear flow. We show that for relatively shorter filaments where the effect of shear and axial stretch is more dominant, the obtained results deviate from the ones based on the classical slender body theory.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-11T06:24:05Z
      DOI: 10.1177/10812865221083323
       
  • Real-form solution for an anisotropic elastic elliptical inhomogeneity
           under uniform heat flux

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      Authors: Xu Wang, Peter Schiavone
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We use the extended Stroh sextic formalism for thermo-anisotropic elasticity to present an elegant solution of the problem of an anisotropic elastic elliptical inhomogeneity embedded in an infinite anisotropic elastic matrix subjected to uniform remote heat flux. We prove rigorously that the remote thermal stresses cannot be set to zero in a generally anisotropic elastic matrix. In particular, a real-form solution is derived for the internal thermoelastic field describing stresses, strains, and displacements within the elliptical inhomogeneity.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-07T04:04:13Z
      DOI: 10.1177/10812865221094503
       
  • Elastodynamics of a coated half-space under a sliding contact

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      Authors: V Bratov, J Kaplunov, SN Lapatsin, DA Prikazchikov
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The paper deals with elastic wave propagating in a layer on a half-space induced by a vertical force. The focus is on the effect of a sliding contact along the interface and its comparative study with a perfect one. The effective boundary conditions substituting the presence of the layer are derived. The leading order term in these conditions corresponds to vertical inertia of the layer, whereas next order correction involves the effect of plate waves in the coating. Analysis of the associated dispersion relation confirms the existence of a Rayleigh-type wave, along with extensional and shear plate waves. An asymptotic hyperbolic-elliptic formulation for surface wave field is also presented. This includes a hyperbolic equation singularly perturbed by a pseudo-differential operator playing a role of a boundary condition for the elliptic equation governing decay over the interior. The sign of the coefficient at the pseudo-differential operator is demonstrated to be always negative, corresponding to a local maximum of the phase speed at zero wave number, and consequently to a distinct receding type of the Rayleigh-type wave quasi-front induced by an impulse load.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-07T03:57:46Z
      DOI: 10.1177/10812865221094425
       
  • Analysis of radial expansion, eversion, and cavitation of soft
           functionally graded material spheres

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      Authors: S Ali Mousavi, Arash Bahrami, Omer San, Romesh C Batra
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We study radial expansion, cavitation, and eversion of spherical shells made of incompressible, isotropic, and functionally graded (i.e. inhomogeneous) soft (or rubber-like) materials that are increasingly being used in prosthetics, seals, tires, flexible electronics, soft robots, and many other applications. We consider all geometric and material nonlinearities and assume the sphere material to be Mooney–Rivlin material whose two parameters, C1(R) and C2(R), are smooth functions of the radial coordinate, R, in the stress-free undeformed configuration. The shell’s inversion illustrates non-uniqueness of solutions in finite elasticity since sphere’s bounding surfaces are traction free in the reference and the deformed configurations but stresses/strains in the interior are different. Assuming that a shell under a dead tensile pressure on the outer surface cavitates when the radial stretch at the inner surface equals four, we delineate effects of functions C1(R) and C2(R) on the cavitation pressure. It is found that for power-law variations with indices m and n, respectively, for C1(R) and C2(R) the cavitation pressure can be controlled by suitably choosing m and n. Large positive and negative values of m and n are deleterious for a sphere loaded only by a pressure on the inner surface since they produce high hoop stresses within the sphere. Other results given in the paper will enable one to tailor functions C1(R) and C2(R) to either mitigate cavitation or initiate it at a desired pressure or have prescribed through-the-thickness variations of stresses to optimize sphere’s performance.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-07T03:53:46Z
      DOI: 10.1177/10812865221093553
       
  • The universal program of linear elasticity

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      Authors: Arash Yavari, Alain Goriely
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Universal displacements are those displacements that can be maintained, in the absence of body forces, by applying only boundary tractions for any material in a given class of materials. Therefore, equilibrium equations must be satisfied for arbitrary elastic moduli for a given anisotropy class. These conditions can be expressed as a set of partial differential equations for the displacement field that we call universality constraints. The classification of universal displacements in homogeneous linear elasticity has been completed for all the eight anisotropy classes. Here, we extend our previous work by studying universal displacements in inhomogeneous anisotropic linear elasticity assuming that the directions of anisotropy are known. We show that universality constraints of inhomogeneous linear elasticity include those of homogeneous linear elasticity. For each class and for its known universal displacements, we find the most general inhomogeneous elastic moduli that are consistent with the universality constrains. It is known that the larger the symmetry group, the larger the space of universal displacements. We show that the larger the symmetry group, the more severe the universality constraints are on the inhomogeneities of the elastic moduli. In particular, we show that inhomogeneous isotropic and inhomogeneous cubic linear elastic solids do not admit universal displacements and we completely characterize the universal inhomogeneities for the other six anisotropy classes.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-07T03:48:54Z
      DOI: 10.1177/10812865221091305
       
  • Modeling the degeneration of the collagen architecture in a
           microstructural model of the human cornea

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      Authors: Anna Pandolfi, Maria Laura De Bellis, Alessio Gizzi, Marcello Vasta
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We propose an enriched micromechanical model of the collagenous reinforcement of the eye stromal tissue. As a departure from an over-simplified model proposed a few years back, where collagen and chemical bonds were modeled as linear-elastic trusses, here we describe the chemical bonds by means of a more realistic generalized Lennard-Jones potential. In keeping with the original model, we disregard the multi-layer nature of the cornea and the continuum nature of the filling elastin matrix. The under-constrained locally orthogonal network of collagen fibrils is stabilized by crosslinks that provide the rigidity of the system and confer the ability to sustain the action of the intraocular pressure. In Ariza-Gracia et al., it has been shown that the weakening and the bulging of the cornea due to ectasia can be ascribed to the reduction of the density of the chemical bonds. The introduction of a pseudo-chemical potential supplies a more realistic model: any mechanical, enzymatic, or chemical cause of the degradation of the tissue observed in ectasia can be effectively introduced in a multi-physic potential, disregarding the adoption of phenomenological models. In numerical calculations, the high non-linearity of the model is suitably controlled by adopting a robust explicit solver based on dynamic relaxation.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-07T03:41:08Z
      DOI: 10.1177/10812865221092690
       
  • On waves in multi-scale chiral elastic systems

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      Authors: Alexander B Movchan, Natalia V Movchan, Ian S Jones
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The paper addresses the question of the dynamic chirality in vibrating elastic systems. An overview of continuous and discrete models is presented with the focus on phenomena, associated with the rotational motion, which are absent in classical non-chiral media. The time dependence is essential for the models discussed in this paper—the effects attributed to the dynamic chirality do not occur in the case of static elastic deformations. A formal connection is also drawn between the mathematical formulations for a class of elastic waves in chiral systems and electromagnetic waves in magnetised media. Both continuum and discrete systems, analysed in the context of the wave localisation and dispersion, are discussed here.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-07T03:38:32Z
      DOI: 10.1177/10812865221091206
       
  • Measurement of two-dimensional residual stress in nanocrystalline
           superelastic NiTi fabricated with pre-strain laser shock peening

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      Authors: Kai Yan, Pengbo Wei, Kangjie Chu, Weifeng He, Chao Yu, Fuzeng Ren, Qingping Sun
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The measurement of residual stress is a challenging issue in industrial fields. In this work, focused ion beam (FIB) and digital image correlation (DIC) are combined together to measure the two-dimensional residual stress in nanocrystalline NiTi plates processed with pre-strain laser shock peening (LSP). A four-point bending experiment verifies the accuracy of this measurement method. The pre-strain LSP-treated surfaces are found to have significant compressive residual stress along the pre-strain direction and tensile residual stress along the vertical to pre-strain direction, which verifies pre-strain LSP as an efficient approach to create gradient residual stress layers in nanocrystalline NiTi plates. The FIB-DIC method has also proven to be an attractive tool to measure the two-dimensional residual stress in phase transition nanocrystalline materials.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-02T08:42:24Z
      DOI: 10.1177/10812865221090589
       
  • Thermoelastic interactions on the propagation of surface waves in a
           piezoelectric half-space: A comparative analysis of GN-III type and
           three-phase-lag model

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      Authors: Sharmistha Rakshit, Anirban Lakshman, Kshitish Ch Mistri
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      This study elucidates the propagation of surface (Rayleigh type) waves in a homogeneous, transversely isotropic, piezothermoelastic half-space subjected to stress free, electrically open or shorted, and thermally insulated or isothermal boundary conditions, based on GN-III type and three-phase-lag thermoelastic models. Plane harmonic wave solutions are employed to find the mechanical displacements, electrical potential, and temperature change. With the aid of these expressions, stresses, electrical displacement, and temperature gradient are derived. Based on different boundary conditions, four secular equations are derived in the considered half-space. Path of the surface particles traces an elliptic path in vertical plane parallel to the direction of wave propagation and the eccentricity of the ellipse is calculated. Particle path degenerates a straight line when there is no phase difference between vertical and horizontal components of displacements. A pre-established analysis is discussed as a particular case of this study. Effect of various characteristics of waves like phase velocity, attenuation coefficient, and specific loss is demonstrated graphically for the GN-III type and three-phase-lag thermoelastic models engaging cadmium selenide (6 mm class) material of hexagonal symmetry. This mathematical framework may be utilized to design and develop temperature sensors, and other piezoelectric surface acoustic wave (SAW) devices.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-05-01T03:40:38Z
      DOI: 10.1177/10812865221092986
       
  • Interfacial delamination-induced unidirectional propagation of guided
           waves in multilayered media

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      Authors: Yanzheng Wang, Zhengyang Li, Mikhail V Golub, Guoliang Huang, Weiqiu Chen, Chuanzeng Zhang
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Unidirectional nonreciprocal wave propagation is an unprecedented phenomenon, which has attracted much research interest. Connecting a phononic crystal with an asymmetric structure to break the spatial inversion symmetry is a popular manner to realize this phenomenon using the wave mode transformation. In this paper, a new model is proposed based on a single periodic structure. The arrays of asymmetric and symmetric interfacial delaminations are intentionally introduced into the top and the bottom part of a stack of periodic elastic layers, respectively. So, the structural spatial inversion symmetry can be broken and the guided waves can pass through the whole structure only from the top side with the changed mode generated by the array of asymmetric interfacial delaminations. Thus, it is indispensable for the part of phononic crystal that the partial band-gaps of symmetric and antisymmetric guided waves have to be separated, which is the reason why we introduce the array of symmetric central or side interfacial delaminations into the stack of periodic elastic layers. The transmission spectra of the guided waves and the dispersion curves for the unit cell imposed by the Bloch–Floquet boundary condition are both calculated by the spectral element method. Then, the interfacial delamination-induced unidirectional propagation of guided waves in the finite stack of periodic elastic layers is numerically confirmed. This paper provides a new concept to control the waves propagating in phononic crystals via the insertion of some interfacial delaminations or cracks.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-29T10:34:50Z
      DOI: 10.1177/10812865221092680
       
  • Asymptotically correct boundary conditions for the higher-order theory of
           plate bending

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      Authors: Maria V Wilde, Maria Yu Surova, Nadezhda V Sergeeva
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The construction of refined boundary conditions for the case of edge loading, corresponding to the theory with modified inertia in respect to the order of asymptotic approximation, is considered. The methods of investigation are based on the works of A. L. Goldenveizer and A. V. Kolos. The solution of three-dimensional (3D) problem is constructed as a superposition of the long-wave approximation and boundary layers. The traction on the edge is presented as generalized Fourier expansions, using the Legendre polynomials. This approach allows to obtain explicit expressions for the coefficients of boundary layers via an iteration procedure, in course of which the boundary conditions are satisfied with a pure asymptotic error. As a result, the refined boundary conditions (RBCs) are constructed. Effective stress resultants and couples are introduced, the coefficients of which (the Goldenveizer–Kolos constants) are the simple polynomial functions of Poisson’s ratio. In addition, the contribution of boundary layers to edge displacements is determined. The comparison of the dispersion curve for the edge wave, calculated on the basis of the theory with modified inertia and RBC, with the 3D solution show good agreement in the 10 times wider frequency range than that of the Kirchhoff’s theory. The same result is obtained for the amplitude of a transient edge wave, excited by edge loading. It is also shown that with making use of RBC one can consider the action of a self-equilibrated edge load in the framework of two-dimensional (2D) theory.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-29T10:28:41Z
      DOI: 10.1177/10812865221088528
       
  • Analysis of a mode-I crack in a one-dimensional orthorhombic quasicrystal
           strip

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      Authors: Keqiang Hu, Weilin Yang, Jiawei Fu, Zengtao Chen, Cun-Fa Gao
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A mode-I crack in a one-dimensional (1D) orthorhombic quasicrystal (QC) strip under in-plane phonon and phason stress loading is considered. Fourier transforms are applied to reduce the mixed boundary value problem of the mode-I crack to solving a system of simultaneous singular integral equations. Asymptotic expressions of the phonon and phason stresses and displacement fields near the crack tips have been obtained in an explicit form. The crack-tip singularities of the mode-I crack have been investigated and the intensity factors of the stresses in the phonon and phason fields are derived explicitly. The stress intensity factors (SIFs) and the hoop stress intensity factors (HSIFs) have been determined to investigate the effect of the geometric size and the crack kinking phenomenon. The effect of the thickness ratio of the cracked strip on the SIFs and energy release rates has been investigated. When the thickness of the cracked strip becomes infinite large, the results obtained for the crack problem can be reduced to the analytic solution for a mode-I crack in an infinite 1D orthorhombic QC media.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-27T09:39:33Z
      DOI: 10.1177/10812865221091748
       
  • Study on the interaction between a screw dislocation and circular holes or
           rigid inclusions by using the angular basis function in conjunction with
           bipolar coordinates

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      Authors: Jeng-Tzong Chen, Shing-Kai Kao, Wei-Chen Tai, Ying-Te Lee, Jia-Wei Lee, Yen-Ting Chou
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, the degenerate kernel in conjunction with the bipolar coordinates is employed to solve the anti-plane problems of interaction between a screw dislocation and circular holes or rigid inclusions. Once the degenerate kernel of the angular basis function (ABF) is provided in terms of the bipolar coordinates, the analytical solution for cases of one or two circular holes and rigid inclusions can be derived. Not only the radial basis function (RBF) but also the ABF is used. First, the observer objectivity of the degenerate kernel in terms of the bipolar coordinates is examined numerically. A special case, one circular hole or rigid inclusion, is considered to demonstrate the validity of the present approach. Finally, the cases containing two circular holes and two circular rigid inclusions were examined. The comparison between available results and ours is well done. Besides, for the solutions of two holes and rigid inclusions, it is interesting to find that the present method provides an analytical solution with a series form of explicitly determined coefficients, while the coefficients provided by the complex variable need to be determined using the recursive formulae.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-26T12:50:10Z
      DOI: 10.1177/10812865221085199
       
  • A general contact stiffness model for elastic bodies and its application
           in time-varying mesh stiffness of gear drive

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      Authors: Hongbing Wang, Changjiang Zhou, Yunyan Lv, Bo Hu
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      As a critical element of time-varying mesh stiffness (TVMS), contact stiffness of a gear drive has been defined based on simplified Hertzian contact stiffness or semi-empirical nonlinear Hertzian contact stiffness in previous works. This study proposes a general contact stiffness model for elastic bodies through piecewise linear interpolation of contact pressure. The TVMS of a spur gear drive is determined through potential energy method and proposed contact stiffness model verified by Hertzian contact theory and finite-element method. Then, the influence of applied load on contact stiffness is studied, and the differences among proposed contact stiffness, simplified Hertzian contact stiffness, and nonlinear Hertzian contact stiffness are analyzed. Results show that contact stiffness increases with the applied load, and the TVMS based on the proposed contact stiffness model is the smallest among the three contact stiffness models. Effects of tooth width and input torque on the TVMS are further discussed. The TVMS becomes bigger with increased tooth width and input torque, but the increase rate decreases as tooth width or input torque increases. These findings indicate that reasonable matching of design parameters is beneficial for increasing load capacity and optimizing the dynamic performance of gear systems.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-21T11:00:21Z
      DOI: 10.1177/10812865221092106
       
  • The energy release rate for non-penetrating crack in poroelastic body by
           fluid-driven fracture

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      Authors: Victor A Kovtunenko, Nyurgun P Lazarev
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A new class of constrained variational problems, which describe fluid-driven cracks (that are pressurized fractures created by pumping fracturing fluids), is considered within the nonlinear theory of coupled poroelastic models stated in the incremental form. The two-phase medium is constituted by solid particles and fluid-saturated pores; it contains a crack subjected to non-penetration condition between the opposite crack faces. The inequality-constrained optimization is expressed as a saddle-point problem with respect to the unknown solid phase displacement, pore pressure, and contact force. Applying the Lagrange multiplier approach and the Delfour–Zolésio theorem, the shape derivative for the corresponding Lagrangian function is derived using rigorous asymptotic methods. The resulting formula describes the energy release rate under irreversible crack perturbations, which is useful for application of the Griffith criterion of quasi-static fracture.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-21T06:17:54Z
      DOI: 10.1177/10812865221086547
       
  • Pitchfork bifurcations in simple hyperelastic orthotropic arterial models
           and their constitutive implications

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      Authors: Cornelius O Horgan, Jeremiah G Murphy
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      This paper is concerned with the response of orthotropic hyperelastic incompressible materials in the homogeneous deformation of simple tension. The problem of out-of-plane simple tension of a cuboid reinforced with two in-plane families of mechanically equivalent initially straight fibres is considered. For this deformation, the material characterisation test where the normal in-plane stresses are equal is examined. Analytical results are obtained for the special case of orthonormal fibres that is where the fibres are initially perpendicular to one another in the undeformed state. It is shown that in this case, there are two distinct solution branches namely the symmetric solution in which the in-plane stretches are equal and an asymmetric solution where this is not the case. The results are illustrated for two specific strain energy densities one of which has been used to model the mechanical response of arteries. For these two models, the asymmetric solution is shown to be energetically favourable at a sufficiently large critical out-of-plane stretch. For small enough out-of-plane stretch, for weakly anisotropic materials, the symmetric solution branch is unique and stable while beyond this critical stretch, this solution is unstable and a pitchfork bifurcation into two stable asymmetric branches is demonstrated. For slight departures from orthonormality of the fibres, a numerical approach is used for one of these models to demonstrate that the response undergoes a significant change. A constitutive restriction is suggested that eliminates the general non-uniqueness demonstrated in this work.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-12T09:30:47Z
      DOI: 10.1177/10812865221084927
       
  • A theoretical scheme for shape-programming of thin hyperelastic plates
           through differential growth

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      Authors: Jiong Wang, Zhanfeng Li, Zili Jin
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, a theoretical scheme is proposed for shape-programming of thin hyperelastic plates through differential growth. First, starting from the 3D governing system of a hyperelastic (neo-Hookean) plate, a consistent finite-strain plate equation system is formulated through a series expansion and truncation approach. Based on the plate equation system, the problem of shape-programming is studied under the stress-free assumption. By equating the stress components in the plate equations to be zero, the explicit relations between the growth functions and the geometrical quantities of target shape of the plate are derived. Then, a theoretical scheme of shape-programming is proposed, which can be used to identify the growth fields corresponding to arbitrary 3D shapes of the plate. To demonstrate the efficiency of the scheme, some typical examples are studied. The predicted growth functions in these examples are adopted in the numerical simulations, from which the target shapes of the plate can be recovered completely. The scheme of shape-programming proposed in the current work is applicable for manufacturing intelligent soft devices.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-07T10:27:27Z
      DOI: 10.1177/10812865221089694
       
  • Plane-polarised finite-amplitude shear waves in deformed incompressible
           materials

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      Authors: Michel Destrade, Giuseppe Saccomandi
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We investigate how two finite-amplitude, transverse, plane body waves may be superposed to propagate in a deformed hyperelastic incompressible solid. We find that the equations of motion reduce to a well-determined system of partial differential equations, making the motion controllable for all solids. We find that in deformed Mooney–Rivlin materials, they may travel along any direction and be polarised along any transverse direction, an extension of a result by Boulanger and Hayes (Quart. J. Mech. Appl. Math. 45 (1992) 575). Furthermore, their motion is governed by a linear system of partial differential equations, making the Mooney–Rivlin special in that respect. We select another model to show that for other materials, the equations are nonlinear. We use asymptotic equations to reveal the onset of nonlinearity for the waves, paying particular attention to how close the propagation direction is to the principal axes of pre-deformation.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-07T10:24:19Z
      DOI: 10.1177/10812865221089588
       
  • Prediction of bone microstructures degradation during osteoporosis with
           fuzzy cellular automata algorithm

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      Authors: Armin Shahmohammadi, Seyedfarzad Famouri, Seyedmohammadreza Hosseini, Maryam Mazraehei Farahani, Mostafa Baghani, Daniel George, Majid Baniassadi
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A novel fuzzy cellular automata is proposed to simulate bone degradation during osteoporosis. The initial three-dimensional (3D) bone microstructure is obtained from computed tomography (CT) images. Cellular automata algorithm is implemented to the 3D lattice and a Sugeno Fuzzy inference system is designed with nine sets of fuzzy rules to simulate the degradation process. A distance vector parameter is defined to describe the number of neighborhood cells that each cell can have a connection with. It is shown that by increasing the value of this distance vector, the results converge toward a quasi-constant degraded microstructure. The obtained microstructure is considered to be the final result and compared to prediction of bone degradation of the literature based on phase exchange calculated from mechanical strain energy. It is shown that the fuzzy cellular automata model predicts a more realistic bone degradation and microstructure distribution than the phase exchange method while having a model significantly simpler.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-07T10:21:37Z
      DOI: 10.1177/10812865221088520
       
  • Equipartition of energy in a helix

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      Authors: Yaswanth Sai Jetti, Martin Ostoja-Starzewski
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      It is well known that the kinetic and potential energies of a system governed by a linear wave equation are equipartitioned in a finite time. This result has been extended by previous researchers to several physical settings: elastodynamics, electrodynamics, and micropolar elasticity. In the case of a helix, there is a direct coupling of longitudinal and torsional wave motions due to the structure of constitutive relations. Providing that the initial conditions functions have compact support, we demonstrate that the equipartition phenomenon occurs after a finite time in this case as well—i.e. the potential energy and the kinetic energy of a helix become equal and remain constant after a finite time.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-07T06:49:16Z
      DOI: 10.1177/10812865221089004
       
  • A phase-field model for thermo-mechanical fracture

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      Authors: Ved Prakash, Akash Kumar Behera, Mohammad Masiur Rahaman
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this article, we propose a thermodynamically consistent phase-field model for thermo-mechanical fracture and provide an open-source implementation of the proposed model using a recently developed finite element toolbox, Gridap in Julia. Here, we have derived the balance equations for the thermo-mechanical fracture by invoking the virtual power principle and determined the constitutive relations for the thermodynamic fluxes based on the satisfaction of the thermodynamic laws. Our proposed formulation provides an equation of temperature evolution that can easily accommodate dissipative effects such as viscous damping. We provide very compact and user-friendly open-source codes for implementing the proposed model using Gridap in Julia that requires very low memory usage and gives a high degree of flexibility to the users in defining weak forms of the governing partial differential equations (PDEs). We have validated the proposed model and its implementation against such standard results available in the literature as crack propagation in the cruciform shape material, single edge notched plate, bi-material beam, and a quenching test.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-07T06:45:45Z
      DOI: 10.1177/10812865221085198
       
  • A PSO-based computational framework to design active noise cancelation
           systems for smart vehicle enclosures

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      Authors: Mojtaba Porghoveh, Kourosh Heidari Shirazi, Antonio Messia, M Erden Yildizdag
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this study, active noise cancelation (ANC) systems are developed by a computational optimization framework based on particle swarm optimization (PSO), aiming to attenuate engine noise inside smart cubic vehicle enclosures. To have rapid estimation of acoustic properties, the main PSO algorithm is coupled with an analytical solution based on modified modal interaction method to evaluate the cost function. The optimum configurations, i.e., best positions and volume velocities of secondary sound sources, are defined for each resonant frequency. For numerical simulations, two vehicle enclosures of different size are considered to assess the applicability of the optimization algorithm. The overall performance of determined ANC systems is investigated, and it is shown that substantial noise reduction is achieved.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-05T09:43:49Z
      DOI: 10.1177/10812865221089376
       
  • Anisotropic stress softening of electromagnetic Mullins materials

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      Authors: MHBM Shariff
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The influence of electromagnetic forces in purely elastic deformable solids has been extensively studied in the literature. However, to the best of the author’s knowledge, the influence of electromagnetic fields on anisotropic Mullins materials has not been studied. In view of this, we propose an anisotropic phenomenological model to describe anisotropic stress softening of electromagnetic Mullins materials; taking note that most materials are not purely elastic and some of them exhibit an anisotropic stress-softening phenomenon widely known as the Mullins effect. The proposed anisotropic model is based on the use of direction-dependent damage parameters and a set of anisotropic spectral invariants, presented recently in the literature by the author. The spectral invariants have a clear physical meaning which is useful in aiding the design of a rigorous experiment to construct a specific form of constitutive equation. Since boundary value results for electromagnetic Mullins materials are not found in the literature, the effect of electromagnetic fields on the Mullins phenomena in simple tension and simple shear deformations is discussed in this paper.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-05T09:41:21Z
      DOI: 10.1177/10812865221082521
       
  • Influence of internal stresses on stability of multilayer micropolar tubes

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      Authors: Denis N Sheydakov
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Within the nonlinear Cosserat continuum, the stability of a compressed multilayer tube under internal and external hydrostatic pressures is studied. The tube is formed by attaching to each other N hollow cylinders that have been subjected to preliminary deformations of axial extension-compression and contains internal stresses. For the model of a physically linear micropolar material, the system of linearized equilibrium equations is derived, which describes the behavior of a multilayer cylindrical tube in a perturbed state. Using a special substitution, the stability analysis is reduced to solving a linear homogeneous boundary-value problem for a system of 6N ordinary differential equations. In the case of a three-layer tube made of dense polyurethane foam, the stability regions were constructed in the planes of loading parameters (the relative axial compression and the relative external or internal pressure) for different preliminary deformations of inner and outer layers (coatings). According to the results obtained, the preliminary extension of both the outer and inner coatings generally stabilizes the considered deformations of the three-layer tube, while the effect of their preliminary compression is negative. It should be noted here that the pre-stressed outer coating has a more significant influence on the tube stability than the pre-stressed inner coating. In addition, the described effects of preliminary deformations are more pronounced for tubes with thicker coatings.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-04T10:28:20Z
      DOI: 10.1177/10812865221086873
       
  • Acoustic radiation from a sphere pulsating near an impedance plane using a
           boundary integral equation method

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      Authors: Burak Üstündağ, M Erden Yildizdag, Bahadır Uğurlu, Ahmet Ergin
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this study, a boundary integral equation method is proposed for investigating acoustic pressure radiation from a sphere pulsating near a free surface or an impedance plane. The half-space and free-space problems are investigated for the acoustic radiation of pulsating sphere. The effects of free surface and impedance boundaries are introduced into the mathematical model by employing three different half-space Green’s functions, respectively. These Green’s functions are derived, respectively, using the single image-source method, multiple equivalent-source method, and complex equivalent-source method. Green’s functions are implemented into the boundary element (BE) formulation. The surface of the pulsating sphere is discretized with linear and quadratic BEs, and the Combined Helmholtz Integral Equation Formulation (CHIEF) is employed to overcome the non-uniqueness problem. Four different case studies are considered for the sphere pulsating near a free surface or an impedance plane. The first case study involves the sphere pulsating near a free surface (perfectly reflective) and the single image-source method is used in the boundary element method (BEM) formulation. In the second case study, the sphere is assumed as pulsating near a perfectly reflecting and perfectly absorbing impedance planes, respectively. The multiple equivalent-source method is employed for the perfectly reflecting plane, but the multiple equivalent-source method and complex equivalent-source methods for the perfectly absorbing plane. The third case study involves a general impedance plane, and all the methods are employed, respectively, in the BE formulation. The final case study assumes a general impedance plane forming a perpendicular incidence and the complex equivalent-source method is used in this particular case. It is observed that there is a very good comparison between the results obtained from all these methods.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-04T10:26:11Z
      DOI: 10.1177/10812865221085196
       
  • An amended approximation of the non-Gaussian probability distribution
           function

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      Authors: Ehsan Darabi, Markus Hillgärtner, Mikhail Itskov
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Network models of rubber elasticity are based on the conformational entropy of an idealized chain and mostly motivated by the non-Gaussian statistical theory by Kuhn and Grün. However, the non-Gaussian probability distribution function cannot be expressed in a closed form and requires an approximation. All such approximations applied in the literature demonstrate pronounced inaccuracies in comparison to the analytical solution. The ideal choice of the approximation function depends on a variety of factors, such as the chain parameters or the desired application of the approximation (the probability distribution function itself, the corresponding entropic energy, or the force developed by the chain). In addition, when making a choice regarding the best approximation for a given application, the applied error measure plays a significant role since the approximation that grants, for example, the best maximal relative error is not necessarily the same that provides the best mean absolute error. In the literature, this application-specific evaluation of available approximations is commonly disregarded. In this paper, we evaluate previously proposed approximations on the application-specific basis and develop an approach to derive a family of approximations for the free energy of a polymer chain in a broader range of the number of its chain segments. The analytical method based on the Padé technique delivers an approximation of the non-Gaussian probability distribution function that can be easily tailored depending on the desired application. The proposed approach is capable to provide much stronger predictions in comparison to the Kuhn and Grün model in a wide range of chain segment numbers.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-04-02T01:02:50Z
      DOI: 10.1177/10812865221083557
       
  • Surface instabilities of soft dielectric elastomers with implementation of
           electrode stiffness

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      Authors: Pietro Liguori, Massimiliano Gei
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      This paper contains a thorough investigation into plane-strain electroelastic surface instabilities of dielectric elastomers. We employ a systematic approach to our investigation, introducing three ways to actuate an elastomer device, namely, actuation by means of (1) attached compliant electrodes, (2) sprayed charges onto the opposite surfaces, and (3) fixed electrodes between which the device “floats” in vacuum and expands transversally. We examine electromechanical instability with particular attention to the third listed mode of actuation and the features of the specimen. We then tackle surface instability for the three modes, showing the relationship between applied pre-stress and the stability domain, as well as the characteristics of the obtained bifurcation fields. The effects of the stiffness of the electrode (relevant in the first listed mode of actuation) on surface instabilities are then investigated by adopting an elastic surface–substrate interaction model in which the properties of the coating enter the boundary conditions for the substrate. Various electrode materials are assumed, demonstrating that their implementation in the model increases the number of solutions at bifurcation and changes the overall stability domain. We present this new enriched bifurcation map, showing the dependence on the wavenumber, and characterise the solutions by examining the bifurcated fields.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-25T06:32:05Z
      DOI: 10.1177/10812865221084309
       
  • Wave propagation in a non-linearly elastic bar with phase transformations

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      Authors: Pingping Zhu, Zheng Zhong
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      There exist considerable difficulties in studying the wave propagation problems of the kind of phase transforming materials with non-monotone material responses due to the lack of uniqueness of solution for a moving phase boundary. An admissibility condition, which is named the Maxwell equal-area criterion, was established from a three-dimensional (3D) internal-variable formulation in the previous study to supplement the one-dimensional (1D) dynamical system of the bars/rods made of the special materials to determine the phase boundary uniquely. In this paper, we employ this criterion to investigate the wave propagation in the bar made of the special kind of phase transforming materials, which are associated with trilinear non-monotone stress–strain responses. The Riemann problem for different boundary states that arises from wave encounters are analyzed by the method of wave curves. Based on the construction of the Riemann solution, we explicitly study the wave propagation in a semi-infinite bar under an impulsive stress impact to explore the dynamical features of the special materials. The wave structures in the entire spatial and temporal domain for two different impact levels are obtained, as well as the state profiles. Detailed analyses and discussions of the wave patterns and wave encounters occurring during the wave propagation process are given for a deep understanding of dynamical phase transitions of the materials. These results are further compared with those obtained using the artificially adopted maximal dissipation rate criterion. The similarities and differences are discussed. The comparisons further confirmed that the special phase transforming material can be used for designing wave-absorption/impact-protection devices.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-25T06:30:46Z
      DOI: 10.1177/10812865221082524
       
  • Approximation of dissipative systems by elastic chains: Numerical evidence

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      Authors: Alberto Maria Bersani, Paolo Caressa, Francesco dell’Isola
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      An old and debated problem in Mechanics concerns the capacity of finite dimensional Lagrangian systems to describe dissipation phenomena. It is true that Helmholtz conditions determine not-always verifiable conditions establishing when a system of n second-order ordinary differential equations in normal form (nODEs) be the Lagrange equations deriving from an nth dimensional Lagrangian. However, it is also true that one could conjecture that, given nODEs it is possible to find a (n+k)th dimensional Lagrangian such that the evolution of suitably chosen n Lagrangian parameters allows for the approximation of the solutions of the nODEs. In fact, while it is well known that the ordinary differential equations (ODEs) usually introduced for describing some dissipation phenomena do not verify Helmholtz conditions, in this paper, we give some preliminary evidence for a positive answer to the conjecture that a dissipative system having n degrees of freedom (DOFs) can be approximated, in a finite time interval and in a suitable norm, by an extended Lagrangian system, having a greater number of DOFs. The theoretical foundation necessary to formulate such a conjecture is here laid and three different examples of extended Lagrangians are shown. Finally, we give some computational results, which encourage to deepen the study of the theoretical aspects of the problem.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-25T06:28:06Z
      DOI: 10.1177/10812865221081851
       
  • Pure bending of an elastic prismatic beam made of a material with
           density-dependent material parameters

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      Authors: Vít Průša, Kumbakonam Ramamani Rajagopal, Alan Wineman
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We investigate the pure bending of an elastic prismatic beam, but unlike in the classical setting we assume that the material parameters are density-dependent. The corresponding boundary value problem admits a semi-analytical solution, and the derived formulae allow one to quickly assess the impact of density-dependent material parameters on the predicted deformation across various parameter regimes, and consequently make a decision on the importance of the density-dependent material parameters in the given setting.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-25T06:26:36Z
      DOI: 10.1177/10812865221081519
       
  • An analytical stress field for bi-material V-notches with end hole: New
           solution and effects of higher order terms

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      Authors: Seyed Karen Alavi, Majid R Ayatollahi, Bahador Bahrami, Morteza Nejati
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Current manuscript develops an analytical stress solution for the bi-material V-notches with an end hole (VO). To do so, based on the Kolosov-Muskhelishvili’s approach, while appropriate potential functions are employed, the boundary conditions of the problem are imposed to the solution to reduce the number of unknown parameters. Subsequently, the analytical stress field is derived as an asymptotic series solution, where each term possessing a constant coefficient and an order of singularity. The order of singularity for each term is obtained from the characteristic equations of the problem which is dependent on the notch geometry and material combinations. The so-called least square method (LSM) is then used to compute the constant coefficients of the asymptotic series for several case studies. Special attention is given to the bi-material notch stress intensity factors (BNSIFs) and the coefficients of the higher order terms (HOTs) in the stress series expansion. The accuracy of the presented stress solution is verified by benchmarking the results with numerical values obtained from finite element (FE) method. In this process, several notch opening angles and notch radii are simulated using the three-point bend (3PB) specimen. The developed asymptotic stress solution is demonstrated to be capable of accurately evaluating the stress field around bi-material VO-notched structures.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-19T05:31:23Z
      DOI: 10.1177/10812865221084311
       
  • Analytical buckling load formulas for cylindrical shell structures with
           variable thickness under non-uniform external pressure

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      Authors: Licai Yang
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The novel contribution of this paper is to develop a quadratic perturbation method to derive general analytical buckling load formulas for cylindrical shell structures with varying wall thickness under non-uniform lateral pressure loads for the first time. Arbitrary thickness and lateral pressure loads are skillfully described and governing differential equations are derived. A quadratic perturbation method is developed to derive buckling load formulas, which establishes the relation among buckling loads, thickness, and load functions. The presented formulas are adequately validated by comparing with recent results for variable wall thickness or non-uniform external pressure, and exhibit a great advantage in determining buckling loads. For the purpose of engineering application, buckling of a cylinder with linear thickness under linear liquid pressure and wind load is deeply studied by the presented formulas. This study can provide a highly efficient method for buckling load computation, and a guide to design the thickness of the shell under non-uniform lateral loads.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-19T05:28:07Z
      DOI: 10.1177/10812865221084105
       
  • An asymptotic modeling and resolution framework for morphology evolutions
           of multiple-period post-buckling modes in bilayers

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      Authors: Chenbo Fu, Zhe Cheng, Ting Wang, Fan Xu
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A stiff thin film bonded to a compliant substrate initially buckles into wrinkles, following with some intricate advanced instability modes when the compression exceeds higher thresholds. Here, we present an asymptotic modeling and resolution framework to quantitatively predict and continuously trace secondary bifurcation transitions in the non-linear post-buckling region. An advantage of this framework, besides its applicability to finite-strain deformations, is its asymptotic consistency with the three-dimensional (3D) field equations and interface continuity conditions in a pointwise manner. Based on our model, we reveal intricate post-buckling responses involving successive advanced mode transitions, i.e., period-doubling, period-tripling, period-quadrupling, ridge, and hierarchical wrinkles in film–substrate bilayers upon excess compression. Apart from modulus ratio, pre-stretch and pre-compression of the substrate can alter surface morphology of film–substrate bilayers. With substrate pre-compression, a bilayer may eventually involve into a period-tripling or period-quadrupling mode. We observe hierarchical wrinkles and ridges in films attached on pre-stretched substrates. With high substrate pre-tension and modulus ratio, a novel pattern, namely, periodic ridges, appears at the secondary bifurcation. Fundamental understanding and quantitative prediction of non-linear morphology evolutions of soft bilayers play important roles in rational designs of wrinkle-tunable functional surfaces.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-17T11:41:08Z
      DOI: 10.1177/10812865221083046
       
  • Sliding frictional contact problem of a layer indented by a rigid punch in
           couple stress elasticity

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      Authors: Isa Çömez, Sami El-Borgi
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      This paper investigates the frictional contact problem of a layer indented by a rigid punch within the framework of the couple stress elasticity. It is assumed that the layer is homogeneous, isotropic, and fully bonded to a rigid substrate. The mixed-boundary value problem is converted using Fourier transform into a singular integral equation in which the unknown is the contact pressure between the layer and the punch. The integral equation is further derived for the flat and cylindrical punch case profiles, normalized and then solved numerically using the Gauss–Jacobi integration formula. The obtained results are first validated based on those published for the case of a frictionless contact problem of a half-plane indented by a rigid punch and solved within the context of couple stress theory. An extensive parametric study is then conducted to investigate the effect of several parameters on the contact stresses for the both the flat and cylindrical punch profiles. These parameters include the characteristic material length, the layer height, the friction coefficient, the indentation load, and the shear modulus.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-17T05:08:59Z
      DOI: 10.1177/10812865221080551
       
  • On variational principles in coupled strain-gradient elasticity

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      Authors: Lidiia Nazarenko, Rainer Glüge, Holm Altenbach
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Strain-gradient elasticity is a special case of high-gradient theories in which the potential energy density depends on the first and second gradient of the displacement field. The presence of a coupling term in the material law leads to a non-diagonal quadratic form of the stored energy, which makes it difficult for the derivation of fundamental theorems. In this article, two variational principles of the minimum of potential and complementary energies are argued in the context of the coupled strain-gradient elasticity theory. The basis of the proofs of both variational principles is the equivalent transformation of the stain and strain-gradient energy density that allows to avoid the complication related to the presence of the fifth-rank coupling tensor [math] in the equation for the potential energy density and leads to diagonalization of the quadratic form of the stored energy. This transformation enables to inverse Hook’s law, to determine compliance tensors, and to obtain closed-form relation for the complementary energy. After that the proofs of both principles of a minimum of potential and complementary energies are provided in the usual manner adopted in the classical theory of elasticity.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-15T12:44:42Z
      DOI: 10.1177/10812865221081854
       
  • On Rayleigh wave field induced by surface stresses under the effect of
           gravity

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      Authors: Ali Mubaraki, Danila Prikazchikov
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The paper is concerned with development of the asymptotic formulation for surface wave field induced by vertical surface stress under the effect of gravity in the short-wave region. The approach relies on the methodology of hyperbolic-elliptic models for the Rayleigh wave and results in a regularly perturbed hyperbolic equation on the surface acting as a boundary condition for the elliptic equation governing decay over the interior. A special value of the Poisson’s ratio v = 0.25 is pointed out, at which the effect of gravity disappears at leading order.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-14T07:02:40Z
      DOI: 10.1177/10812865221080550
       
  • Stochastic Zener model with complex order fractional derivatives

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      Authors: Teodor Atanacković, Stevan Pilipović, Dora Seleši
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We analyze the dissipation inequality for the constitutive equation of a complex order fractional Zener model and obtain appropriate thermodynamical restrictions for the wave-type model equation in terms of its Laplace transform. These constraints obtained on the model parameters are less restrictive than the ones known in the previous literature. The main results of this paper are related to explicitly solving this equation in spaces of tempered distributions, proving the existence and uniqueness of the solution and discussing its regularity properties. The second set of results is related to the analysis of including random perturbations such as white noise in the model resulting in stochastic wave propagation models. We analyze various stochastic body forces, random initial excitations, and random initial velocities as input data followed by deriving the stochastic solution and calculating its most important statistical characteristics. All these results significantly extend our previous results related to a real order fractional Zener model.MSC[2020]: 26A33, 35L05, 35R11, 35R60, 60G10, 60G15, 74D05, 74J05, 82D30
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-07T12:15:17Z
      DOI: 10.1177/10812865221080736
       
  • Static condensation of peridynamic heat conduction model

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      Authors: Yakubu Kasimu Galadima, Erkan Oterkus, Selda Oterkus
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A model order reduction methodology for reducing the order of the peridynamic transient heat model is proposed. This methodology is based on the static condensation procedure. To set the development of the model reduction procedure on a sound mathematical setting, a nonlocal vector calculus was employed in the formulation of the heat transport problem. The model order reduction framework proposed in this study provides a technique to reduce the dimensionality of a peridynamic transport model while still maintaining accurate prediction of the model response. Moreover, the methodology can be adaptively applied to accommodate different resolution requirements for different sections of the model. Using numerical experiments, the proposed methodology is shown to be capable of accurately reproducing results of the full peridynamic transient heat transport problem.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-05T09:48:59Z
      DOI: 10.1177/10812865221081160
       
  • Second-gradient continua: From Lagrangian to Eulerian and back

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      Authors: Francesco dell’Isola, Simon R Eugster, Roberto Fedele, Pierre Seppecher
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, we represent second-gradient internal work functionals in Lagrangian (referential) and Eulerian (spatial) descriptions, and we deduce the corresponding expressions for the Piola transformations of stress and double-stress tensors and of external forces and double-forces. We also derive, in both the Eulerian and Lagrangian description, the expression of surface and edge contact interactions (which include forces and double-forces) for second-gradient continua in terms of the normal and the curvature of contact boundary surfaces and edge shapes.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-05T09:44:00Z
      DOI: 10.1177/10812865221078822
       
  • Laplace domain BEM for anisotropic transient elastodynamics

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      Authors: Ivan Markov, Leonid Igumnov, Aleksandr Belov, Victor Eremeyev
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained. Boundary elements with mixed approximation of geometry and field variables with the standard nodal collocation procedure are used for spatial discretization. In order to obtain time-domain solutions, the classic Durbin’s method is applied for numerical inversion of Laplace transform. Problem of alleviating Gibbs oscillations is addressed. Dynamic boundary element analysis of the model problem involving trigonal material is performed to test presented formulation. Obtained results are compared with finite element solutions.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-04T12:50:48Z
      DOI: 10.1177/10812865221078202
       
  • Critical velocities and displacements of anisotropic tubes under a moving
           pressure

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      Authors: Xin-Lin Gao, Andrew G Littlefield
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Critical velocities and middle-surface displacements of anisotropic axisymmetric cylindrical shells (tubes) under a uniform internal pressure moving at a constant velocity are derived in closed-form expressions by using the Love–Kirchhoff thin shell theory incorporating the rotary inertia and material anisotropy. The formulation is based on the general three-dimensional constitutive relations for orthotropic elastic materials and provides a unified treatment of orthotropic, transversely isotropic, cubic and isotropic tubes, which can represent various composite and metallic tubes. Closed-form formulas are first obtained for the general case with both the rotary inertia and radial stress effects, which are then reduced to the special cases without the rotary inertia effect and/or radial stress effect. It is shown that when the rotary inertia effect is suppressed and the radial normal stress is neglected, the newly derived formulas for the critical velocities of orthotropic and isotropic tubes recover the two existing ones for thin tubes as special cases. An example for an isotropic tube is provided to illustrate the new formulas, which give the values of the critical velocity and dynamic amplification factor that agree well with those obtained experimentally and computationally by others.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-04T12:48:55Z
      DOI: 10.1177/10812865221077454
       
  • Development, implementation, and assessment of a continuum model of
           anisotropic behavior of polycrystalline materials due to texture using a
           second-order structure tensor

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      Authors: Brandon C Templin, Adetokunbo A Adedoyin, Koffi Enakoutsa, Douglas J Bammann
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      An Evolving Micro-structural Model of Inelasticicty is modified to capture evolving anisotropy resulting from underlying texture. Anisotropy is modeled via a second-order orientation tensor resulting from the truncation to second order of an orientation distribution function and the temporal evolution of the tensor arises naturally from the closure properties associated with the truncation. A scalar variable defined by the Euclidean norm of the current state of the structure tensor and the direction of the rate of continuing plastic deformation is incorporated in the flow rule. The model predictions is compared with yield surface data after various preloads for Aluminum 1100-O, differences in compression versus torsion for 304L SS, and large directional changes in load path for AL 1100-O. Additional assessments of the model which compared the predictions of the model with and without textural effects are provided.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-03-04T05:32:59Z
      DOI: 10.1177/10812865211073076
       
  • Nonlocal vibration of functionally graded nanoplates using a layerwise
           theory

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      Authors: Mohamed-Ouejdi Belarbi, Li Li, Mohammed Sid Ahmed Houari, Aman Garg, Hanuman Devidas Chalak, Rossana Dimitri, Francesco Tornabene
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      This work studies the size-dependent free vibration response of functionally graded (FG) nanoplates using a layerwise theory. The proposed model supposes not only a higher-order displacement field for the core but also the first-order displacement field for the two face sheets, thereby maintaining an interlaminar displacement continuity among layers. Unlike the conventional layerwise models, the number of variables is kept fixed and does not increase for an increased number of layers. This is a very important feature compared to conventional layerwise models and facilitates significantly the engineering analyses. The material properties of the FG nanoplate are graded continuously through the thickness direction in accordance with a power-law function. The Eringen’s nonlocal elasticity theory is here adopted to relax the continuum axiom required in classical continuum mechanics and hence hopeful to capture the small size effects of naturally discrete nanoplates. The equations of motion of the problem are obtained via a classical Hamilton’s principle. The present layerwise model is implemented with a computationally efficient C0- continuous isoparametric serendipity elements and applied to solve a large-scale discrete numerical problem. The robustness and reliability of the developed finite element model are demonstrated by a comparative evaluation of results against predictions from literature. The comparative studies show that the proposed finite element model is: (a) free of shear locking, (b) accurate with a fast rate convergence for both thin and thick FG nanoplates, and (c) excellent in terms of numerical stability. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanoplates to the aspect ratio, length-to-thickness ratio, nonlocal parameter, boundary conditions, power-law index, and modes shapes. Referential results are also reported, for the first time, for natural frequencies of FGM nanoplates which will serve as benchmarks for further computational investigations.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-24T09:57:30Z
      DOI: 10.1177/10812865221078571
       
  • Some entropy-related properties of thermoelastic materials

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      Authors: Ali Khoeini, Ali Imam
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Non-classical thermoelastic materials are studied in the framework of continuum thermodynamics. Using “Part I” of the second law of thermodynamics in the classical formulation of continuum thermodynamics, the existence of the entropy function for various classes of non-classical thermoelastic materials is established. Also, a function known as the internal rate of production of entropy is defined for the classical and non-classical thermoelastic materials and is subsequently used to obtain a balance law for the entropy. Finally, using the Clausius inequality as “Part II” of the second law of thermodynamics, some results regarding the constitutive response functions for the thermoelastic materials are obtained.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-23T11:43:50Z
      DOI: 10.1177/10812865221078862
       
  • Maxwell–Eshelby relation in Cosserat elasticity theory

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      Authors: Milad Shirani
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this work, using quasiconvexity and rank-one convexity conditions in Cosserat elasticity theory, we derive the Maxwell–Eshelby relation for Cosserat bodies with a surface of discontinuity.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-14T05:46:31Z
      DOI: 10.1177/10812865221077456
       
  • An open-source implementation of a phase-field model for brittle fracture
           using Gridap in Julia

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      Authors: Mohammad Masiur Rahaman
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      This article proposes an open-source implementation of a phase-field model for brittle fracture using a recently developed finite-element toolbox, Gridap in Julia. This work exploits the advantages of both the phase-field model and Gridap toolbox for simulating fracture in brittle materials. On one hand, the use of the phase-field model, which is a continuum approach and uses a diffuse representation of sharp cracks, enables the proposed implementation to overcome such well-known drawbacks of the discrete approach for predicting complex crack paths as the need for re-meshing, enrichment of finite-element shape functions, and an explicit tracking of the crack surfaces. On the other hand, the use of Gridap makes the proposed implementation very compact and user-friendly that requires low memory usage, and provides a high degree of flexibility to the users in defining weak forms of partial differential equations. Tests on a single-edge notched plate under tension, an L-shaped panel, a notched plate with a hole, a notched beam under symmetric three-point bending and a notched beam with three holes under asymmetric three-point bending are considered to demonstrate how the proposed Gridap-based phase-field Julia code can be used to simulate fracture in brittle materials.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-12T12:09:44Z
      DOI: 10.1177/10812865211071088
       
  • Erratum, Characterization of the symmetry class of an elasticity tensor
           using polynomial covariants

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      Authors: Marc Olive, Boris Kolev, Rodrigue Desmorat, Boris Desmorat
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.

      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-10T08:35:34Z
      DOI: 10.1177/10812865221074926
       
  • Indentation of a periodically layered, elastic half-space by a rigid
           sphere

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      Authors: Deepak Sachan, Ishan Sharma, T Muthukumar
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We investigate indentation by a smooth, rigid, spherical indenter of a heterogeneous half-space made up of layers of two different linear-elastic materials arranged periodically, parallel to the free surface. We utilize homogenization theory to approximate the heterogeneous material by a linear-elastic, homogeneous, but transversely isotropic material. This replaces the original system by an analytically tractable indentation problem, whose solution is then compared with that of the former obtained through the finite element (FE) method. We find that the contact pressure obtained through homogenization is a good approximation to that on the layered half-space, and the approximation improves if (1) the layer thickness is reduced, or (2) the indented force is augmented, or (3) the two layers exhibit closer elastic response. We demonstrate that the difference between the pressures obtained from FE and homogenization has an upper bound that depends only upon the materials’ Poisson’s ratio, the ratio of their Young’s moduli, and their volume fractions. We then show that the penetration depth of the indenter in the layered half-space converges to that in the homogenized material as the layers become thinner. Finally, we find that the homogenized material captures well the discontinuous variation of von Mises stress in the layered medium.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-10T08:33:40Z
      DOI: 10.1177/10812865221074302
       
  • A non-classical theory of elastic dielectrics incorporating couple stress
           and quadrupole effects: part II - variational formulations and
           applications in plates

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      Authors: Yilin Qu, Ziwen Guo, Feng Jin, Gongye Zhang
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A new Mindlin plate model is developed incorporating the couple stress, quadrupole, and curvature-based flexoelectric effects using a non-classical elastic dielectric theory. The general governing equations and complete boundary conditions are derived simultaneously through a variational approach. The new general plate model includes the model for centrosymmetric materials as a special case. As direct applications of the new plate and to illustrate the flexoelectric effect, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the new centrosymmetric model. The numerical results reveal that the flexoelectric effect is present in centrosymmetric materials and is important when the plate thickness is very thin. The dispersion relations for flexure and fundamental shear modes are obtained. We find electrostatic wave also propagates with the flexure or fundamental shear waves by flexoelectric coupling. The present work can be seen as an extension of mechanical analysis of plate structures with couple stress effects and may be useful to the devices design of micro- or nano-sized objects.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-08T05:50:32Z
      DOI: 10.1177/10812865221075768
       
  • Modeling of an energy harvester with porous piezoelectric/piezomagnetic
           nanocomposite structure

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      Authors: Tao Fan
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      Micro-energy harvesters are attracting more and more attention due to the demand of the miniaturization and the self-power for the electrical devices. A three-layered porous piezoelectric (PE)/piezomagnetic (PM) energy harvester at the nanoscale is modeled in this paper. The layered PE/PM structure works in the magnetic field; the electrical power can be obtained from the PE layer due to the magnetostriction of the PM layers. Based on the surface elasticity and Boit’s porous theory, the governing equations and the analytical expressions of the harvester with the thickness-shear mode are derived. The numerical analysis indicates that the electrical energy capture capability of the porous PE/PM energy harvester is much superior to its nonporous alternative. Then, the influences of the porous properties, the surface effects, and the constitution of the PE/PM materials on the energy capture performance are discussed. The results indicate that the nano PE/PM energy harvester with pores can be controlled and optimized by improving the porous, surface, and geometrical parameters.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-08T05:47:03Z
      DOI: 10.1177/10812865221075732
       
  • Exact solutions of the theory of elasticity for a clamped rectangle

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      Authors: Mikhail D Kovalenko, Irina V Menshova, Alexander P Kerzhaev, Guangming Yu
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We present the formulas that describe the exact solutions of the boundary value problems in the theory of elasticity for a half-strip and a rectangle in which the horizontal sides are firmly clamped, while normal and tangential stresses are specified on the vertical ones. We consider only an even-symmetric deformation of the half-strip and the rectangle relative to the horizontal axis of symmetry as well as even-symmetric and odd-symmetric deformations relative to the vertical axis of symmetry for the rectangle. This paper is based on the previously obtained solutions for a free half-strip and a free rectangle.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-04T10:00:43Z
      DOI: 10.1177/10812865221075360
       
  • Bending of clamped orthotropic thin plates: polynomial solution

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      Authors: Dmitriy P Goloskokov, Alexander V Matrosov
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, we study the bending of a clamped thin orthotropic plate by the Bubnov–Galerkin method. Special-type polynomials constructed on the basis of classical Jacobi polynomials and satisfying the clamped conditions are used as basis functions. The “quasi-orthogonality” property of first and second derivatives of the polynomials allows us to immediately write out the formula for the deflection of the plate in the form of a series, by analogy with the Navier method for a free-supported isotropic plate. This solution approximates well the displacement of the plate, but the series for moments and shear forces do not give reliable results. The refusal of using the “quasi-orthogonality” property of the polynomials leads to the solution of an infinite system of linear algebraic equations for finding unknown coefficients of series. The resulting series give reliable results for both displacements and moments and shear forces. The convergence of the series for displacement is very good, but it worsens for shearing forces and bending moments.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-02T10:12:46Z
      DOI: 10.1177/10812865221075280
       
  • Interfacial wave propagation in initially stressed compressible
           hyperelastic materials

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      Authors: Moniba Shams, Kanwal Ejaz
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, the propagation of interfacial waves at the joint boundary of two initially stressed compressible half-spaces is discussed. The materials are subject to pure homogeneous strain and the wave is assumed to travel along one of the principle axes. For mathematical formulation of the problem, non-linear theory of elasticity and theory of invariants are used. Boundary conditions at the interface are applied which lead to an implicit secular equation governing the wave speed. A prototype strain-energy function is used for specialized theoretical results to understand the physical behavior of waves at the interface. A special case of biaxial initial stress is considered and the results are presented theoretically and graphically for representative numerical values of parameters. It is observed that the wave speed is considerably affected by intrinsic properties, i.e., material parameters as well as the amount of initial stress.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-02T10:10:26Z
      DOI: 10.1177/10812865221074304
       
  • Axisymmetric necking versus Treloar–Kearsley instability in a
           hyperelastic sheet under equibiaxial stretching

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      Authors: Mi Wang, Lishuai Jin, Yibin Fu
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We consider bifurcations from the homogeneous solution of a circular or square hyperelastic sheet that is subjected to equibiaxial stretching under either force- or displacement-controlled edge conditions. We derive the condition for axisymmetric necking and show, for the class of strain-energy functions considered, that the critical stretch for necking is greater than the critical stretch for the Treloar–Kearsley (TK) instability and less than the critical stretch for the limiting-point instability. An amplitude equation for the bifurcated necking solution is derived through a weakly nonlinear analysis and is used to show that necking initiation is generally sub-critical. Abaqus simulations are conducted to verify the bifurcation conditions and the expectation that the TK instability should occur first under force control, but when the edge displacement is controlled, the TK instability is suppressed, and it is the necking instability that will be observed. It is also demonstrated that axisymmetric necking follows a growth/propagation process typical of all such localization problems.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-02-02T06:02:00Z
      DOI: 10.1177/10812865211072897
       
  • Non-symmetric indentation of an elastic half-plane

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      Authors: Sandip Saha, Apurba Narayan Das
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this work, the problems of wave propagation in a half-space due to the indentation by a rigid wedge at a constant speed and by a parabolic punch at a constant acceleration have been considered separately. The elastodynamics problems of non-symmetric indentation over a contact region expanding at a constant speed and constant acceleration have been solved using the method of homogeneous functions. Following Cherepanov and Cherepanov et al., the general solution of the problems has been derived in terms of an analytic function of complex variables. The expressions for the stress component under the contact region and the torque over the contact region have been derived. Numerical results of the particular cases of the Problems I and III and of the Problems II and IV have been presented in the form of graphs. This work and its applications are expected to be helpful in the study of indentation-related problems of solid mechanics.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-31T08:31:41Z
      DOI: 10.1177/10812865211073978
       
  • Analysis of an anti-plane crack in a one-dimensional orthorhombic
           quasicrystal strip

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      Authors: Keqiang Hu, Weilin Yang, Jiawei Fu, Zengtao Chen, Cun-Fa Gao
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, a central crack in a one-dimensional (1D) orthorhombic quasicrystal strip under anti-plane loadings has been studied. Fourier transform is applied to reduce the mixed boundary value problem of the crack to solving a system of simultaneous singular integral equations. Asymptotic expressions of the phonon and the phason fields near the crack tips have been obtained. The crack-tip singularities of the anti-plane crack have been investigated, and the intensity factors of the stresses in the phonon and the phason fields are derived explicitly. The stress intensity factors (SIFs) and the hoop stress intensity factors (HSIFs) have been determined to investigate the effect of the geometric size and the crack skewing phenomenon. This crack skewing phenomenon is different from the mode-III crack problems in isotropic elastic materials and transversely isotropic elastic materials where the crack propagates along the original crack plane.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-31T08:29:17Z
      DOI: 10.1177/10812865211073814
       
  • Veering of Rayleigh–Lamb waves in orthorhombic materials

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      Authors: Andrea Nobili, Bariş Erbaş, Cesare Signorini
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      We analyse veering of Rayleigh–Lamb waves propagating in a plane of elastic symmetry for a thin orthotropic plate. We demonstrate that veering results from interference of partial waves in a similar manner as it occurs in systems composed of one-dimensional (1D) structures, such as beams or strings. Indeed, in the neighbourhood of a veering point, the system may be approximated by a pair of interacting tout strings, whose wave speed is the geometric average of the phase and group velocity of the relevant partial wave at the veering point. This complementary pair of partial waves provides the coupling terms in a form compatible with a action–reaction principle. We prove that veering of symmetric waves near the longitudinal bulk wave speed repeats itself indefinitely with the same structure. However, the dispersion behaviour of Rayleigh–Lamb waves are richer than that of 1D systems, and this reflects also on the veering pattern. In fact, the interacting tout string model fails whenever the dispersion branch is not guided by either partial wave. This often occurs when neighbouring veering points interact and partial waves no longer provide guiding curves.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-25T05:54:24Z
      DOI: 10.1177/10812865211073467
       
  • Characteristic foliations of material evolution: from remodeling to aging

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      Authors: Víctor Manuel Jiménez, Manuel de León, Marcelo Epstein
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      For any body-time manifold [math] there exists a groupoid, called the material groupoid, encoding all the material properties of the material evolution. A smooth distribution, the material distribution, is constructed to deal with the case in which the material groupoid is not a Lie groupoid. This new tool provides a unified framework to deal with general non-uniform material evolution.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-18T04:54:09Z
      DOI: 10.1177/10812865211066122
       
  • Modeling of three-dimensional beam nonlinear vibrations generalizing
           Hencky’s ideas

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      Authors: Emilio Turco
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-17T06:17:09Z
      DOI: 10.1177/10812865211067987
       
  • On solvability of initial boundary-value problems of micropolar elastic
           shells with rigid inclusions

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      Authors: Victor A Eremeyev, Leonid P Lebedev, Violetta Konopińska-Zmysłowska
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated and studied. It is proved a theorem of existence and uniqueness of a weak solution for the problem under consideration.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-16T05:40:40Z
      DOI: 10.1177/10812865211073149
       
  • Impact response of a thin shallow doubly curved linear viscoelastic shell
           rectangular in plan

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      Authors: Marina V Shitikova
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      In this paper, we consider the problem on a transverse impact of a viscoelastic sphere upon a viscoelastic shallow doubly curved shell with rectangular platform, the viscoelastic features of which are defined via the fractional derivative standard linear solid models; in so doing, only Young’s time-dependent operators are preassigned, while the bulk moduli are considered to be constant values, since the bulk relaxation for the majority of materials is far less than the shear relaxation. Shallow panel’s displacement subjected to the concentrated contact force is found by the method of expansion in terms of eigen functions, and the sphere’s displacement under the action of the contact force, which is the sum of the shell’s displacement at the place of contact and local bearing of impactor and target’s materials, is defined from the equation of motion of the material point with the mass equal to sphere’s mass. Within the contact domain, the contact force is defined by the modified Hertzian contact law with the time-dependent rigidity function. For decoding the viscoelastic operators involving the problem under consideration, the algebra of Rabotnov’s fractional operators is employed. A nonlinear integro-differential equation is obtained either in terms of the contact force or in the local bearing of the target and impactor materials. Using the duration of contact as a small parameter, approximate analytical solutions have been found, which allow one to define the key characteristics of impact process.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-16T05:36:44Z
      DOI: 10.1177/10812865211072902
       
  • Screw dislocation pileups in a two-phase thin film

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      Authors: Ping Yang, Xu Wang, Peter Schiavone
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The method of continuously distributed dislocations is used to study the distribution of screw dislocations in a linear array piled up near the interface of a two-phase isotropic elastic thin film with equal thickness in each phase. The resulting singular integral equation is solved numerically using the Gauss–Chebyshev integration formula to arrive at the dislocation distribution function and the number of dislocations in the pileup.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-13T09:20:37Z
      DOI: 10.1177/10812865211072895
       
  • Two-field variational formulations for a class of nonlinear mechanical
           models

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      Authors: Andaluzia Matei, Madalina Osiceanu
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      A nonlinear boundary value problem arising from continuum mechanics is considered. The nonlinearity of the model arises from the constitutive law which is described by means of the subdifferential of a convex constitutive map. A bipotential [math], related to the constitutive map and its Fenchel conjugate, is considered. Exploring the possibility to rewrite the constitutive law as a law governed by the bipotential [math], a two-field variational formulation involving a variable convex set is proposed. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-10T09:29:34Z
      DOI: 10.1177/10812865211066123
       
  • Homogenization of the wave equation with non-uniformly oscillating
           coefficients

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      Authors: Danial P. Shahraki, Bojan B. Guzina
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The focus of our work is a dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g., functionally graded) media endowed with periodic microstructure. For this class of quasi-periodic medium variations, we pursue homogenization of the scalar wave equation in [math], [math], within the framework of multiple scales expansion. When either [math] or [math], this model problem bears direct relevance to the description of (anti-plane) shear waves in elastic solids. By adopting the lengthscale of microscopic medium fluctuations as the perturbation parameter, we synthesize the germane low-frequency behavior via a fourth-order differential equation (with smoothly varying coefficients) governing the mean wave motion in the medium, where the effect of microscopic heterogeneities is upscaled by way of the so-called cell functions. In an effort to demonstrate the relevance of our analysis toward solving boundary value problems (deemed to be the ultimate goal of most homogenization studies), we also develop effective boundary conditions, up to the second order of asymptotic approximation, applicable to one-dimensional (1D) shear wave motion in a macroscopically heterogeneous solid with periodic microstructure. We illustrate the analysis numerically in one dimension by considering (i) low-frequency wave dispersion, (ii) mean-field homogenized description of the shear waves propagating in a finite domain, and (iii) full-field homogenized description thereof. In contrast to (i) where the overall wave dispersion appears to be fairly well described by the leading-order model, the results in (ii) and (iii) demonstrate the critical role that higher-order corrections may have in approximating the actual waveforms in quasi-periodic media.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-04T06:20:00Z
      DOI: 10.1177/10812865211065098
       
  • Nonlinear deformations of a cylindrical pipe with pre-stressed thin
           coatings

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      Authors: Leonid Zubov, Mikhail Karyakin
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      The paper presents an exact solution for the problem of large deformations of torsion, axial tension–compression, and radial expansion or shrinkage of an elastic hollow circular cylinder equipped with pre-stressed elastic coatings. Surface coatings are modeled using the six-parameter nonlinear shell theory. The constitutive material of the cylinder is described by a three-dimensional nonlinear model of the isotropic incompressible body of the general form. Special boundary conditions describe the interaction of this material with thin coatings on the inner and outer surface of the pipe. Based on the solution obtained, numerical calculations were performed on the effect of preliminary stresses in coatings on the stress–strain state of a cylindrical pipe.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-04T05:35:22Z
      DOI: 10.1177/10812865211063507
       
  • Predicting peak stresses in microstructured materials using convolutional
           encoder–decoder learning

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      Authors: Ankit Shrivastava, Jingxiao Liu, Kaushik Dayal, Hae Young Noh
      First page: 1336
      Abstract: Mathematics and Mechanics of Solids, Ahead of Print.
      This work presents a machine-learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective response and overall structure of stress fields. However, their ability to predict peak – which are of critical importance to failure – is unexplored, because the peak-stress clusters occupy a small spatial volume relative to the entire domain, and hence require computationally expensive training. This work develops a deep-learning-based convolutional encoder–decoder method that focuses on predicting peak-stress clusters, specifically on the size and other characteristics of the clusters in the framework of heterogeneous linear elasticity. This method is based on convolutional filters that model local spatial relations between microstructures and stress fields using spatially weighted averaging operations. The model is first trained against linear elastic calculations of stress under applied macroscopic strain in synthetically generated microstructures, which serves as the ground truth. The trained model is then applied to predict the stress field given a (synthetically generated) microstructure and then to detect peak-stress clusters within the predicted stress field. The accuracy of the peak-stress predictions is analyzed using the cosine similarity metric and by comparing the geometric characteristics of the peak-stress clusters against the ground-truth calculations. It is observed that the model is able to learn and predict the geometric details of the peak-stress clusters and, in particular, performed better for higher (normalized) values of the peak stress as compared to lower values of the peak stress. These comparisons showed that the proposed method is well-suited to predict the characteristics of peak-stress clusters.
      Citation: Mathematics and Mechanics of Solids
      PubDate: 2022-01-04T06:22:20Z
      DOI: 10.1177/10812865211055504
       
 
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