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European Journal of Mechanics - A/Solids

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ISSN (Print) 0997-7538
Published by Elsevier

[2565 journals]

Fractional order generalized electro-magneto-thermo-elasticity
- Abstract: Publication date: Available online 9 June 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): Yajun Yu , Xiaogeng Tian , Tian Jian Lu
  Built upon the fractional order generalized thermoelasticity (FOGTE), which is based on ETE (extended thermoelasticity), a fractional order generalized electro-magneto-thermo-elasticity (FOGEMTE) theory is developed for anisotropic and linearly electro-magneto-thermo-elastic media by introducing the dynamic electro-magnetic fields, with various generalized thermoelasticity considered, such as ETE, TRDTE (temperature rate dependent thermoelasticity), TEWOED (thermoelasticity without energy dissipation), TEWED (thermoelasticity with energy dissipation), DPLTE (dual-phase-lag thermoelasticity). The two temperature (thermodynamics and conductive temperature) model is also introduced. In addition, to numerically deal with the multi-physics problems expressed by a series of partial differential equations especially a fractional one, the corresponding variational principle based on the variational integral method is proposed, and various degenerated variational theorems are presented. A generalized variational theorem is obtained for the unified theory by using the semi-inverse method. Finally, two examples are numerically validated, and concluding remarks are also given.
  
  PubDate: 2013-06-12T00:35:28Z
Analysis of air-inflated, heavy, membrane tube supported at two points on an incline
- Abstract: Publication date: Available online 6 June 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): Yoon-Rak Choi
  In this study, the cross section of an air-inflated heavy membrane structure anchored at two points on an inclined foundation is examined. Novel general solutions obtained in a previous study for air-inflated membrane structures are used to solve the problem in this work. By imposing boundary conditions on the general solutions, unknown values are formulated as solutions to algebraic equations. The shape and characteristic values are mathematically expressed in closed form. The cross-sectional area is also evaluated analytically. Some results for the characteristic values and shapes are ultimately presented.
  
  PubDate: 2013-06-08T00:37:42Z
On a Nanoscopically-Informed Shell Theory of Single-Wall Carbon Nanotubes
- Abstract: Publication date: Available online 4 June 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): Chandrajit Bajaj , Antonino Favata , Paolo Podio–Guidugli
  This paper proposes a bottom-up sequence of modeling steps leading to a nanoscopically informed macroscopic theory of single-walled carbon nanotubes (SWCNTs). We provide a description of the geometry and the mechanics of the two most representative types of SWCNTs, armchair (A-) and zigzag (Z-), of their modules and of their elementary bond units. We believe ours to be the simplest shell theory that accounts accurately for the linearly elastic response of both A- and Z- CNTs; its main novel feature is perhaps the proposition of chirality-dependent concepts of effective thickness and effective radius, whose evaluation is achieved in terms of nanoscopic information; moreover, as shown in the companion paper [13], it can be generalized to fit SWCNTs of whatever chirality.
  
  PubDate: 2013-06-08T00:37:42Z
Experimental Characterization, Modeling and Parametric Identification of the Non-Linear Dynamic Behavior of Viscoelastic Components
- Abstract: Publication date: Available online 3 June 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): Hanen Jrad , Jean Luc Dion , Franck Renaud , Imad Tawfiq , Mohamed Haddar
  The aim of this paper is to investigate non linear dynamic behavior of viscoelastic components. The dynamic characteristics of viscoelastic components depend on frequency, amplitude, preload, and temperature. A Non Linear Generalized Maxwell Model (NLGMM), with only 4 independent parameters, is proposed. The NLGMM is based on the separation between the linear viscoelasticity and the non linear stiffness. This assumption is validated on a large range of experimental measures. The NLGMM can be used for different kinds of excitations in non linear dynamics: periodic, transient or random excitations. The non linear stiffness is represented by a simple polynomial function. Comparisons between measures and computed values have been carried on several viscoelastic samples. The NLGMM shows a good accordance with experimental results.
  
  PubDate: 2013-06-04T02:00:35Z
The effect of shear strength on the ballistic response of laminated composite plates
- Abstract: Publication date: November–December 2013
  Source:European Journal of Mechanics - A/Solids, Volume 42
  Author(s): K. Karthikeyan , B.P. Russell , N.A. Fleck , H.N.G. Wadley , V.S. Deshpande
  The ballistic performance of clamped circular carbon fibre reinforced polymer (CFRP) and Ultra High Molecular Weight Polyethylene (UHMWPE) fibre composite plates of equal areal mass and 0/90° lay-up were measured and compared with that of monolithic 304 stainless steel plates. The effect of matrix shear strength upon the dynamic response was explored by testing: (i) CFRP plates with both a cured and uncured matrix and (ii) UHMWPE laminates with identical fibres but with two matrices of different shear strength. The response of these plates when subjected to mid-span, normal impact by a steel ball was measured via a dynamic high speed shadow moiré technique. Travelling hinges emanate from the impact location and travel towards the supports. The anisotropic nature of the composite plate results in the hinges travelling fastest along the fibre directions and this results in square-shaped moiré fringes in the 0/90° plates. Projectile penetration of the UHMWPE and the uncured CFRP plates occurs in a progressive manner, such that the number of failed plies increases with increasing velocity. The cured CFRP plate, of high matrix shear strength, fails by cone-crack formation at low velocities, and at higher velocities by a combination of cone-crack formation and communition of plies beneath the projectile. On an equal areal mass basis, the low shear strength UHMWPE plate has the highest ballistic limit followed by the high matrix shear strength UHMWPE plate, the uncured CFRP, the steel plate and finally the cured CFRP plate. We demonstrate that the high shear strength UHMWPE plate exhibits Cunniff-type ballistic limit scaling. However, the observed Cunniff velocity is significantly lower than that estimated from the laminate properties. The data presented here reveals that the Cunniff velocity is limited in its ability to characterise the ballistic performance of fibre composite plates as this velocity is independent of the shear properties of the composites: the ballistic limit of fibre composite plates increases with decreasing matrix shear strength for both CFRP and UHMWPE plates.
  
  PubDate: 2013-05-31T00:37:44Z
Free Vibration of Functionally Graded Beams with Arbitrary Number of Surface Cracks
- Abstract: Publication date: Available online 23 May 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): Kamil Aydin
  Free vibration of beams made of functionally graded materials (FGMs) containing any arbitrary number of open edge cracks is studied. The study is based on Euler-Bernoulli beam and massless rotational springs connecting two intact segments of the beam. It is assumed that the material gradients follow exponential distribution through beam thickness direction. Frequency equations are obtained for flawed FGM beams with fixed-fixed, fixed-hinged, fixed-free, hinged-hinged, and spring-spring end boundaries. Detailed parametric investigation is carried out to examine the influences of crack depth, crack location, total number of cracks, material property distribution, and boundary conditions on the natural frequencies of the damaged FGM beams. The frequency equation for a damaged FGM beam with any kind of two end supports and any arbitrary number of cracks are established through a third order determinant. Compared to previous studies, this decrease in the determinant order can lead to significant advantages in the computational time.
  
  PubDate: 2013-05-27T00:34:48Z
Full field analysis of three dimensional piezoelectric layered half-space with point loading
- Abstract: Publication date: Available online 23 May 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): Ru-Li Lin
  In this study, a three dimensional transversely isotropic piezoelectric layered half-space subjected to concentrated loading and electric charge was analyzed. This paper provides an effective analytical methodology to obtain the explicit full-field solutions for this problem. Due to the dissimilar structures of the solutions, the applied loadings are separated into axis-symmetric loadings and non-symmetric loadings. By using the double Fourier transformation technique in conjunction with series expansion, the explicit closed-from solutions for displacements, stresses, and the electric field in the layered half-space are obtained. The analytical solutions are valid for loadings applied either in the interior or at the surface of the structure. It can be seen that the complete solutions obtained by the method used in this study comprise only the fundamental solutions of an infinite space with a concentrated loading. One of the fundamental solutions is the Green’s function of an infinite space and the others are solutions induced to satisfy the boundary and interface conditions. The mathematical meaning of the method used in the study is in fact the image method or Mindlin’s superposition method. Instead of finding image singularities manually, the intensity and locations of the image singularities are determined automatically from the mathematical technique used in this paper. Taking PZT materials as an example, the numerical computation for the full-field distributions of the displacement and electric field in the layered half-space medium subjected to a point force and a point charge was discussed.
  
  PubDate: 2013-05-27T00:34:48Z
Stability analysis for transverse breathing cracks in rotor systems
- Abstract: Publication date: November–December 2013
  Source:European Journal of Mechanics - A/Solids, Volume 42
  Author(s): Chaozhong Guo , Mohammad A. AL-Shudeifat , Jihong Yan , Lawrence A. Bergman , D. Michael McFarland , Eric A. Butcher
  Transverse breathing cracks have been considered a primary mode of damage in studies of rotordynamic systems. In this paper, a Jeffcott rotor with a transverse breathing crack is examined, and stability of the system is investigated by Floquet theory considering the crack depth and rotating speed. New breathing functions proposed in a recent publication are adopted to approximate the actual breathing mechanism of the crack. Unlike previous studies wherein stability diagrams without detailed information about the stable and unstable regimes of the motion have been provided, in this work we perform a detailed study of the corresponding eigenvalues of the cracked rotor in the complex plane, and the effect of damping on the instability regions has been investigated. Our study indicates that the unstable regions appear as the speed of the rotor approaches an integer fraction or an integer multiple of the critical speed of the rotor, whereas bifurcations are detected in certain unstable regimes. The results also shows damping has significant influence on the structures of instability regions.
  
  PubDate: 2013-05-23T00:35:47Z
Dynamic Characteristics of Damped Viscoelastic Nonlocal Euler-Bernoulli Beams
- Abstract: Publication date: Available online 15 May 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): Y. Lei , T. Murmu , S. Adhikari , M.I. Friswell
  The dynamic characteristics of damped viscoelastic nonlocal beams are studied in this paper. The Kelvin-Voigt and three-parameter standard viscoelastic models, velocity-dependent external damping and nonlocal Euler-Bernoulli beam theory are employed to establish the governing equations of motion for the bending vibration of nanobeams. A transfer function method (TFM) is developed to obtain closed-form and uniform solution for the vibration analysis of Euler-Bernoulli beams with different boundary condition. New analytical expressions for critical viscoelastic parameters, damping parameters and limiting frequencies are obtained. Considering a carbon nanotube as a numerical example, the effects of the nonlocal and viscoelastic constants on the natural frequencies and damping factors are discussed. The results demonstrate the efficiency of the proposed modeling and analysis methods for free vibration analysis of viscoelastic damped nonlocal Euler-Bernoulli beams.
  
  PubDate: 2013-05-19T00:35:02Z
Editorial board
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  
  PubDate: 2013-05-15T00:39:30Z
A moisture diffusion coupled model for composite materials
- Abstract: Publication date: Available online 14 May 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): D. Gueribiz , F. Jacquemin , S. Fréour
  In this study, a coupled diffusive behavior model for a polymer matrix composite is proposed. Within this model, the diffusion of moisture depends upon the stress state experienced by the material. The model constitutive equations are based on a thermo-dynamical approach. The model is, firstly, established for a homogeneous isotropic matrix. It is, thereafter, extended to impermeable unidirectional composites. The stress-diffusion relation has been treated through a two steps procedure. In a first step, only the coupling between the maximum moisture absorption capacity and the stresses is assumed to occur. This implicitly involves that the diffusivity remains independent upon the mechanical states. In a second step, both the diffusivities and maximum moisture absorption capacity were expressed as functions of the mechanical states.
  
  PubDate: 2013-05-15T00:39:30Z
A non-uniform transformation field analysis for frictional cohesive geomaterials
- Abstract: Publication date: Available online 7 May 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): T. Jiang , J.F. Shao , W.Y. Xu
  This paper is devoted to the micromechanical analysis of effective behavior of heterogeneous materials with pressure-dependent plastic constituents. The micromechanical model is based on an extension of the NTFA method proposed by Michel and Suquet (2003, 2004). The local plastic strain field is divided into a volumetric part and a deviatoric part. Each part is expressed as a linear combination of relevant non-uniform plastic strain fields, called “plastic modes”. The non-uniform microscopic strain fields are thus described by a finite number of reduced internal variables. And the local constitutive models are then reformulated in terms of such variables. The proposed model is applied to two typical heterogeneous materials: inclusion reinforced composite and porous material. Numerical results obtained by the NTFA are compared with the direct finite element solutions. In particular, the macroscopic yield stresses of porous materials are compared between the NTFA and some recently proposed analytical criteria. Finally, as an application example, the micromechanical model is used to simulate laboratory tests performed on porous sandstone.
  
  PubDate: 2013-05-11T00:39:10Z
A non-classical Mindlin plate finite element based on a modified couple stress theory
- Abstract: Publication date: Available online 7 May 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): Bo Zhang , Yuming He , Dabiao Liu , Zhipeng Gan , Lei Shen
  This paper presents a novel Mindlin plate element based on the framework of modified couple stress theory for static bending, free vibration and buckling analysis of non-classical Mindlin micro-plates using the first-order shear deformation theory. The proposed non-classical Mindlin plate element has four nodes with 36-DOF (degrees of freedom) in which the in-plane displacements are not considered, satisfying the C 0 continuity and weak C 1 continuity. Unlike the classical Mindlin plate element, this plate element contains one material length scale parameter and can be directly used to predict the size effect. The formulations for modeling the micro-plates are derived in detail. Finite element formulations are obtained by using the weak form equations of the Mindlin micro-plates. To illustrate the applicability and accuracy of the Mindlin plate element, the problems of static bending, free vibration and buckling for rectangular micro-plates with various boundary conditions are investigated. Convergence studies are also carried out to examine the reliability and accuracy of the numerical solutions. It is shown that the typical numerical results are in good agreement with available analytical solutions and numerical solutions reported in previous literatures. In addition, the numerical results show that the size effect in Mindlin micro-plates can be effectively predicted with the proposed plate element. The predicted size effects are similar to the experimental observations in wire torsion and foil bending
  
  PubDate: 2013-05-11T00:39:10Z
Observations on Mode I Ductile Tearing in Sheet Metals
- Abstract: Publication date: Available online 9 May 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): S.A. El-Naaman , K.L. Nielsen
  Cracked ductile sheet metals, subject to Mode I tearing, has been observed to display a variety of fracture surface morphologies depending on the material properties, and a range of studies on the fracture surface appearance has been published in the literature. Whereas classical fractures such as cup-cone, cup-cup and slanting are widely observed, the phenomenon of a slanted crack which systematically “flips” back and forth in a roughly 45° orientation has only recently been reported. The present study aims to add details and understanding to this crack growth phenomenon - through experimental testing and comparison with published results. A series of crack propagation tests have been carried out, where cracks are driven many plate thicknesses under global Mode I loading. The current study employs both the edge crack specimen (ECS) loaded in combined in-plane bending and extension, and the double edge notched tension (DENT) specimen loaded in extension. Clear evidence of the alternating slant failure is observed for a normal strength steel and details on the phenomenon are brought out by grinding and polishing cross-sections in successive steps along the crack growth direction. Moreover, these results are compared to a soft aluminum (1050A) which predominantly shows cup-cup or slant failure. In general, both materials fail by the mechanism of void growth to coalescence (fractographs are included), and evidence point towards cup-cup being favored by materials that experience extensive amounts of void growth (thus severe thinning in the process zone), whereas slanting is typical in high strength materials that rapidly nucleate large populations of smaller voids.
  
  PubDate: 2013-05-11T00:39:10Z
Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants
- Abstract: Publication date: Available online 4 May 2013
  Source:European Journal of Mechanics - A/Solids
  Author(s): J.G. Murphy
  Skeletal muscles, ligaments and tendons are typically assumed to be incompressible, transversely isotropic, nonlinearly hyperelastic materials. If one adopts the phenomenological approach to modelling, then the corresponding strain-energy function can be represented as an arbitrary function of two invariants of the Cauchy-Green strain tensors, representing the isotropic contribution, and two pseudo-invariants, representing the anisotropic contribution. For mathematical convenience, dependence on one of these pseudo-invariants is usually dropped. It will be shown here that a necessary consequence of this reduced form of the strain-energy function is that the infinitesimal shear moduli are identical, an assumption that is not supported by experimental data. It will also be shown that a further consequence is that two out of the three shearing modes are identical over the full range of deformation. The conclusion is that transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants.
  
  PubDate: 2013-05-07T00:38:50Z
A 2D finite element implementation of the Fleck–Willis strain-gradient flow theory
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  Author(s): Kim Lau Nielsen , Christian Niordson
  The lay-out of a numerical solution procedure for the strain gradient flow (rate-independent) theory by Fleck and Willis [A mathematical basis for strain-gradient theory – Part II: Tensorial plastic multiplier, 57:1045–1057; 2009, JMPS] has been an open issue, and its finite element implementation is yet to be completed. Only recently, a sound solution procedure that allows for elastic–plastic loading/unloading and the interaction of multiple plastic zones has been put forward, and demonstrated within a 1D model set-up. The aim of the present work is to extend this procedure to form a basis for 2D and 3D calculations, and thereby to broaden its use within engineering applications. Focus is on the numerical implementation that adopts image analysis techniques to identify individual plastic zones and to treat none-regular mesh configurations. The developed finite element model is demonstrated through; i) tensile loading of a finite homogeneous material slab that offers a simple interpretation of results, ii) tensile loading of a double edge notch tension specimen involving symmetry considerations, and iii) shearing of a periodically voided structure that displays the ability of the procedure to treat periodic boundary conditions. A comparison between the implemented flow theory model and the corresponding rate-dependent visco-plastic version of the model shows coinciding results in the limit of zero rate-sensitivity.
  
  PubDate: 2013-05-07T00:38:50Z
Thermal buckling of functionally graded skew and trapezoidal plates with different boundary conditions using the element-free Galerkin method
- Abstract: Publication date: November–December 2013
  Source:European Journal of Mechanics - A/Solids, Volume 42
  Author(s): E. Jaberzadeh , M. Azhari , B. Boroomand
  In this paper, thermal buckling of functionally graded skew and trapezoidal plates is investigated using the element-free Galerkin method. The shape functions are constructed using the moving least squares (MLS) approximation and the essential boundary conditions are introduced into the formulation through the use of the Lagrange multiplier method and the orthogonal transformation techniques. The material properties are assumed to vary as a power form of the thickness coordinate. Uniform, Linear and nonlinear temperature rise across the thickness are considered. The effects of aspect ratio, thickness ratios, gradient index and skew angle on the critical buckling temperature difference are examined.
  
  PubDate: 2013-05-03T00:42:18Z
Interaction between wedge disclination dipoles and core–shell nanowires with interface effects
- Abstract: Publication date: November–December 2013
  Source:European Journal of Mechanics - A/Solids, Volume 42
  Author(s): Yingxin Zhao , Qihong Fang , Youwen Liu , Nong Zhang
  In order to understand the influence of disclinations on mechanical properties of nanostructured composite materials, the interaction between a wedge disclination dipole and core–shell nanowires with interface effects is investigated. By using the complex variable method, the analytical solutions of complex potentials are derived for the interaction of a wedge disclination dipole and a core–shell nanowire considering interface effects. The stress fields, the elastic strain energy and the force acting on the wedge disclination dipole center are obtained. The influence of the feature of disclination dipole, the nanoscale coating thickness, the uniform eigenstrain and the material elastic dissimilarity on the equilibrium location and the stability of the dipole is studied when the size of the core–shell nanowire is reduced to nanometer scale. The results show that the impact of interface stresses on the equilibrium and the motion of the dipole near the core–shell nanowire is significant, namely, interface stresses have important effect on the strengthening and toughening of the nanostructured composite materials. The material properties of coating layer are dominant factors in the influence of the equilibrium location and the stability of disclination dipole for serious mismatch (i.e. very hard or very soft) and/or thick coating layer.
  
  PubDate: 2013-05-03T00:42:18Z
Pull-in instability of cantilever and fixed–fixed nano-switches
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  Author(s): Nazita Taghavi , Hassan Nahvi
  In this article, pull-in instability of cantilever and fixed–fixed nano-switches subjected to electrostatic forces produced by an applied voltage, and intermolecular forces are investigated. A linear distributed load model is considered to approximately model the nonlinear intermolecular and electrostatic interactions acting on the nano-beam. The effect of small length-scale is taken into account using hybrid nonlocal Euler–Bernoulli beam model. The effects of small length-scale on the pull-in instability and freestanding behavior of the cantilever and fixed–fixed nano-beams are presented and compared with the Eringen's nonlocal and classical beam models. It is found that the Eringen's nonlocal beam model produces unreasonable pull-in voltages, minimum gaps and detachment lengths. It is shown that shortcomings of the Eringen's nonlocal beam theory can be resolved by using hybrid nonlocal beam model.
  Graphical abstract
  
  PubDate: 2013-04-25T00:39:42Z
A new laminated composite beam element based on eigenvalue problem
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  Author(s): Nam-Il Kim , Chan-Ki Jeon , Jaehong Lee
  A new laminated composite beam element is developed based on the eigenvalue problem for the flexural and torsional analyses of beams with I- and channel-sections. Analytical technique is used to present the laminated composite beam theory considering the transverse shear and the restrained warping induced shear deformation based on an orthogonal Cartesian coordinate system. From the energy principle, the equilibrium equations are derived and the member stiffness matrix is determined using the force–displacement relations of the beam. In order to demonstrate the validity of this study, the deflections and the twist angles of composite beams with I- and channel-sections are presented and compared with the results from other researchers and the finite beam element using the Lagrange interpolation functions, and the detailed finite element analysis results using ABAQUS. Especially the flexural and torsional behavior and the effect of shear deformation are investigated with respect to the modulus ratio and the fiber angle change.
  
  PubDate: 2013-04-21T00:40:29Z
An opening crack model for thermopiezoelectric solids
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  Author(s): Xian-Ci Zhong , Ke-Shi Zhang
  In previous studies of thermoelectroelastic analysis for a cracked thermopiezoelectric solid, the crack-face thermal boundary condition is always assumed to be fully insulated or conductive. The effects of applied electromechanical loadings on the thermal stress field near crack tip have not been widely considered. In the present paper, the thermal-medium crack model is applied to simulate an opening crack in a thermopiezoelastic solid, which is filled with a dielectric. The heat flux and electric displacement at the crack surfaces are assumed to be dependent on crack opening displacement. Applying the Fourier transform technique, the thermal stress field in full plane is determined explicitly in terms of the elementary functions. The effects of applied electromechanical loadings and the thermal conductivity inside a crack on the normalized thermal stress intensity factor and crack center opening displacement are investigated through numerical results and shown in graphics. The observations reveal that the thermal stress intensity factor depends not only on applied thermal loadings but also on applied electromechanical loadings, the thermal conductivity and dielectric permittivity of crack interior.
  
  PubDate: 2013-04-21T00:40:29Z
Surface/interface effects on elastic behavior of an edge dislocation in the shell of a core–shell nanowire
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  Author(s): M.Yu. Gutkin , S. Rezazadeh Kalehbasti , H.M. Shodja
  The elastic behavior of an edge dislocation placed in the shell of a free-standing core–shell nanowire is considered within the theory of surface/interface elasticity. Using the method of complex potential functions the expressions for the stress field of the dislocation, image forces on the dislocation, and the dislocation strain energy are derived and studied in detail. A special attention is paid to non-classical effects revealed within the surface/interface elasticity approach where a characteristic length parameter referred to as surface/interface modulus is introduced. These effects are (i) the stress oscillations along the shell surface and core–shell interface for negative values of the surface/interface elastic moduli; (ii) a strong dependence of image forces on the core size; (iii) extra repelling (attraction) of the dislocation from (to) the shell surface and core–shell interface characterized by positive (negative) interface modulus; and (iv) a decrease of the dislocation strain energy in the central region of the shell and its local increase with an extra maximum in the vicinity of the shell surface for negative values of the surface/interface elastic moduli. These non-classical effects increase with diminishing core radius and shell thickness and are very strong in the layers of 1 nm thickness adjacent to the core–shell interface and shell surface. The effects of the residual surface stress are also addressed.
  
  PubDate: 2013-04-17T00:42:18Z
Two-dimensional theory of piezoelectric plates considering surface effect
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  Author(s): Chunli Zhang , Weiqiu Chen , Ch. Zhang
  Two-dimensional (2D) equations of piezoelectric plates with nano-thickness are obtained, which take account of the surface effect. The piezoelectric plate is treated as a bulk core plus two surface layers. The influence on the plate's overall properties resulted from the surface piezoelectricity is modeled by a spring force exerting on the boundary of the bulk core. Using the derived 2D equations, the Miller–Shenoy coefficients and the natural frequencies of the nano-piezoelectric plate for pure extensional deformations are first analyzed. The performance of a nano-piezoelectric plate harvester is then investigated theoretically. Numerical results show that the effective properties and the natural frequencies of the plate are size-dependent, and the nano-piezoelectric harvester exhibits a stronger ability of converting mechanical energy into electric energy than the traditional macro- or micro-structures.
  
  PubDate: 2013-04-17T00:42:18Z
Laminated beam analysis by polynomial, trigonometric, exponential and zig-zag theories
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  Author(s): E. Carrera , M. Filippi , E. Zappino
  A number of refined beam theories are discussed in this paper. These theories were obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials, trigonometric series, exponential, hyperbolic and zig-zag functions. The Finite Element method is used to derive governing equations in weak form. By using the Unified Formulation introduced by the first author, these equations are written in terms of a small number of fundamental nuclei, whose forms do not depend on the expansions used. The results from the different models considered are compared in terms of displacements, stress and degrees of freedom (DOFs). Mechanical tests for thick laminated beams are presented in order to evaluate the capability of the finite elements. They show that the use of various different functions can improve the performance of the higher-order theories by yielding satisfactory results with a low computational cost.
  
  PubDate: 2013-04-17T00:42:18Z
A numerical approach for the establishment of strain gradient constitutive relations in periodic heterogeneous materials
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  Author(s): Jia Li , Xiao-Bing Zhang
  In this work, we developed a new numerical approach for the establishment of strain gradient constitutive equations in heterogeneous materials with periodic microstructure through homogenization over a unit cell. To this end, we considered a periodic unit cell of finite size, including different homogenous phases and subjected to gradient remote loading. The local elasticity problem was solved by combining the theoretical asymptotic analysis with the Fast Fourier Transform (FFT) method. The asymptotic analysis allows the establishment of differential equations of different orders. These equations were resolved by using the FFT method. By using the homogenization procedure proposed in Li (2011a,b), intrinsic strain gradient constitutive relations can be constructed. This approach fulfils the severe exigency on accuracy of the high-order homogenization. Numerical simulations on examples with 1D and 2D microstructures showed that this approach is highly accurate and efficient. Discussions were completed on the mechanical implications of the strain gradient constitutive laws through the obtained numerical results.
  
  PubDate: 2013-04-17T00:42:18Z
Moving polarization saturation crack in ferroelectric solids
- Abstract: Publication date: September–October 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  
  A moving polarization saturation (PS) model is proposed to study the plane problem of a Yoffe-type crack moving with constant velocity in ferroelectric materials considering electric saturation. Based on the extended Stroh formalism, the model is solved using complex function method. The closed-form expressions for the electroelastic fields are obtained in a concise way. Results are shown to converge to known solutions for static PS model and the moving linear piezoelectric model. Numerical results for PZT-5H material are given graphically. It can be deducted that the dynamic intensity factors are dependent of the electric field and the velocity. It predicts that crack propagation may be promoted by a positive applied electrical field and inhibited by the negative one. For high crack velocity, 0.28 times minimum body wave speed, the hoop stress is maximal for an angle θ ≠ 0 .
  Highlights ► We propose the moving polarization saturation model in ferroelectric materials. ► Dynamic intensity factors of stress, electric displacement are obtained. ► Results converge to static PS model and the moving linear piezoelectric model. ► Dynamic intensity factors of stress are dependent of electric field and velocity.
  
  PubDate: 2013-04-13T00:38:41Z
Editorial board
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  PubDate: 2013-04-05T09:39:40Z
Nonlocal elasticity theory for radial vibration of nanoscale spherical shells
- Abstract: September–October 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  
  This paper presents the radial vibration of nanoscale spherical shells based on the nonlocal elasticity theory. The shell is considered elastic, homogeneous and isotropic. The nonlocal differential equation of radial motion is derived in terms of radial displacement. The relation between the nonlocal and local frequencies is also investigated. Considering the small-scale effect, the general characteristic equation for radial vibration of spherical shell is obtained by applying boundary conditions. Moreover, the characteristic equations for two special cases are presented. To demonstrate the accuracy of the present formulation, theoretical calculations of the fundamental frequency have been compared with those available in the literature and a good agreement is achieved. The variations of the frequencies with the nonlocal parameter, radius ratio and Poisson's ratio are also examined. It is observed that the frequencies are affected when the size effect is taken into consideration.
  
  PubDate: 2013-04-05T09:39:40Z
Finite inflation of an initially stretched hyperelastic circular membrane
- Abstract: September–October 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  
  In this paper, finite axisymmetric inflation of an initially stretched flat circular hyperelastic membrane has been analyzed. The membrane material has been assumed to be a homogeneous and isotropic Mooney–Rivlin solid. The inflation problem has been reduced to a set of three first order ordinary differential equations using a set of appropriately defined variables. An interesting method based on the invariance of these equations to scaling has been used to solve the two point boundary value problem without much effort. This method does not require any special technique for negotiating the limit points in the pressure–stretch relations of the membrane. Several inflation results of an initially unstretched and pre-stretched circular membrane for various material parameters are obtained. The roles of pre-stretch and internal pressure on the inflation mechanics are clearly delineated. The initial stretch is observed to have some interesting counter-intuitive effects on the inflation of the membrane.
  
  PubDate: 2013-04-01T00:40:40Z
Wave propagation in stiffened structures using spectrally formulated finite element
- Abstract: September–October 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  
  In this work, the wave propagation analysis of built-up composite structures is performed using frequency domain spectral finite elements, to study the high frequency wave responses. The paper discusses basically two methods for modeling stiffened structures. In the first method, the concept of assembly of 2D spectral plate elements is used to model a built-up structure. In the second approach, spectral finite element method (SFEM) model is developed to model skin-stiffener structures, where the skin is considered as plate element and the stiffener as beam element. The SFEM model developed using the plate–beam coupling approach is then used to model wave propagation in a multiple stiffened structure and also extended to model the stiffened structures with different cross sections such as T-section, I-section and hat section. A number of parametric studies are performed to capture the mode coupling, that is, the flexural–axial coupling present in the wave responses.
  Highlights ► We model wave propagation in built-up composite structures. ► The model use frequency domain based spectral finite element method (SFEM). ► Plate–beam coupling is introduced in SFEM to model stiffened structures. ► Wave propagation analysis is performed for multiple stiffened structures. ► Wave responses are obtained for stiffened structures with T, I or Hat section.
  
  PubDate: 2013-03-28T01:38:35Z
Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion
- Abstract: September–October 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 41
  
  In this paper, the buckling problem of thin rectangular functionally graded plates subjected to proportional biaxial compressive loadings with arbitrary edge supports is investigated. Classical plate theory (CPT) based on the physical neutral plane is applied to derive the stability equations. Mechanical properties of the FGM plate are assumed to vary continuously along its thickness according to a power law function. The displacement function is considered to be in the form of a double Fourier series whose derivatives are determined using Stokes' transformation. The advantage of this method is capability of considering any possible combination of boundary conditions with no necessity to be satisfied in the Fourier series. To give generality to the problem, the plate is assumed to be elastically restrained by means of rotational and translational springs at the four edges. Numerical examples are presented, and the effects of the plate aspect ratio, the FGM power index, and the loading proportionality factor on the buckling load of an FGM plate with different usual boundary conditions are studied. The present results are compared with those have been previously reported by other analytical and numerical methods, and very good agreement is seen between the findings indicating validity and accuracy of the proposed approach in the buckling analysis of FGM plates.
  Highlights ► We studied the buckling of thin rectangular FGM plates with arbitrary edge supports. ► Classical plate theory (CPT) based on the physical neutral plane was applied. ► We exploited Fourier series as displacement function and using Stokes' transformation. ► The buckling load increases by more constraining of the plate edges. ► The present method can be extended to buckling as well as vibration analysis of beams and shells.
  
  PubDate: 2013-03-28T01:38:35Z
On the three-phase-lag linear micropolar thermoelasticity theory
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  The constitutive laws for the three-phase-lag micropolar thermoelasticity theory are given. The uniqueness and reciprocal theorems are proved and a variational principle is established for a linear micropolar anisotropic and inhomogeneous thermoelastic solid. A continuous dependence result is given for isotropic solid.
  
  PubDate: 2013-03-24T01:35:02Z
On the transformation behavior of functionally graded SMA composites subjected to thermal loading
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  Shape Memory Alloy (SMA) composites are being used in an ever-expanding set of applications. For new applications, Functionally Graded (FG) SMA composites are being developed incorporating a wide variety of matrices. An analytical methodology combining averaging technique of composites and an SMA constitutive model is developed to determine the transformation properties of the FG–SMA composite. The results obtained from the analyses of such a composite show that after transformation the stress in the SMA composite is lower than in the case of pure elastic composite under the same thermal loading. This decrease in stress can result in an increase in temperature resistance and improved mechanical properties of SMA composites. This work will be explored through a parametric study to understand their influence on SMA composites design.
  Highlights ► The transformation properties of the FG–SMA composite are determined. ► The constitutive model of the FG–SMA composite is developed. ► The averaging technique of composites and an SMA constitutive model are combined. ► Results show that stress in the FG–SMA composite is lower than the pure elastic case.
  
  PubDate: 2013-03-16T01:35:50Z
Closed-form solution for elliptical inclusion problem in antiplane piezoelectricity with far-field loading at an arbitrary angle
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  An elliptical piezoelectric inclusion embedded in an infinite piezoelectric matrix is analyzed in the framework of linear piezoelectricity. Using the conformal mapping technique, a closed-form solution is obtained for the case of a far-field antiplane mechanical load, τ 0, and an inplane electrical load, E 0, at an arbitrary angle β. The stress and electric field distribution patterns for different defect shapes, loading angles, and material constants are studied. The energy release rates of self-similarly expanding and rotating defects in the presence of an electric field are obtained using the generalized M- and L-integrals as a function of the loading angle. The physical significance of these results is discussed in terms of the stress and electric field distributions as well as the energy release rates.
  Highlights ► Antiplane piezoelectricity. ► Closed-form solution for elliptical inclusion problem. ► Stress and electric field distribution and concentration. ► Self-similar expansion force (M-integral) and Material moment (L-integral). ► Sensitivity and reliability of electromechanical devices.
  
  PubDate: 2013-03-16T01:35:50Z
One-dimensional constitutive SMA model with two martensite variants: Analytical and numerical solutions
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  This paper deals with the one-dimensional modeling of a shape memory alloy (SMA) in order to reproduce the special thermo-mechanical response of the material. In particular, new analytical solutions are developed using a simple one-dimensional SMA model based on the introduction of three phases: tensile martensite, compressive martensite and austenite; the ability to reproduce the pseudo-elastic and shape memory effects; the different behavior in tension and compression; the different elastic properties of the three phases; and the reorientation process of the martensite. The model assumes the martensite volume fractions as internal variables, whose evolution is governed by stress and temperature. Analytical solutions, which take into consideration the axial loads and thermal processes, are developed to solve the axial problem. Furthermore, a numerical procedure is developed in order to time-integrate the kinetic laws that rule the evolution of the internal variables during the phase transformations and a 2-node finite element beam is implemented. Considering the constant and non-constant elastic properties for the three SMA phases, some applications are presented in order to verify the effectiveness of the proposed model and the analytical and numerical solutions. Comparisons with experimental data related to the axial response of SMA wires and laminae are carried out. Finally, a numerical application concerning a SMA lamina, which is subjected to bending load at high temperatures inducing the pseudo-elastic effect in the material, is presented.
  Highlights ► New analytical solutions are proposed based on a 1D SMA model. ► The model reproduces the pseudo-elastic and the shape memory effects. ► Tension–compression asymmetry and variants reorientation are considered. ► Analytical and numerical solutions are given for axial loads and thermal processes. ► Applications considering constant and non-constant elastic properties are presented.
  
  PubDate: 2013-03-16T01:35:50Z
Shakedown analysis of 90-degree mitred pipe bends
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  The behaviours of smooth 90-degree pipe bends under cyclic loading have received substantial attention in recent years where shakedown and ratchetting domains have been determined. However, such data are considerably lacking for mitred pipe bends. In the current research, the lower bound shakedown limit loads of 90-degree mitred pipe bends are determined via a simplified direct non-cyclic numerical technique recently developed by Abdalla et al. (2007) The analysed mitred pipe bends are subjected to the combined effect of steady internal pressures and cyclic in-plane or out-of-plane bending moments. Both in-plane closing and opening bending moment cases are considered. The shakedown boundaries of three mitred pipe bend geometries with one, two, and three welded joints are determined and compared with the shakedown boundary of a smooth 90-degree pipe bend. All analysed bends have diameter to thickness ratio of 25 and bend radius of 1.5 times the pipe mean diameter. The results indicate that the shakedown boundaries of mitred bends have reduced domains compared with the smooth pipe bend of similar geometrical parameters. Shakedown domains of mitred bends increase in size as the number of welded joints increase until it approaches the shakedown boundary of the smooth pipe bend simulating a mitred bend with infinite number of welded joints. The percentage of the area under shakedown domain for the mitred pipe bends to that of the smooth pipe bend ranges from 20% for the single mitred pipe bend to 75% for the 3-weld mitred bend. Results also revealed that reducing the number of mitred welded joints, dominates reversed plasticity response at the expense of ratchetting response. Out-of-plane bending generally showed larger shakedown domain than the in-plane bending shakedown domain. Additionally, the shakedown domains for in-plane closing and opening moments are quite similar.
  Highlights ► The shakedown behaviour of mitred pipe bends compared to smooth pipe bend. ► The analysis includes both closing and opening in-plane bending types. ► Out-of-plane bending usually introduces higher shakedown boundaries than in-plane. ► Single and 2-weld mitred pipe bends exposed more to the reversed plasticity. ► As the number of welds increase the ratchetting failure mode becomes more significant.
  
  PubDate: 2013-03-16T01:35:50Z
The influence of void size on the micropolar constitutive properties of model heterogeneous materials
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  In this paper the mechanical behaviour of model heterogeneous materials consisting of regular periodic arrays of circular voids within a polymeric matrix is investigated. Circular ring samples of the materials were fabricated by machining the voids into commercially available polymer sheet. Ring samples of differing sizes but similar geometries were loaded using mechanical testing equipment. Sample stiffness was found to depend on sample size with stiffness increasing as size reduced. The periodic nature of the void arrays also facilitated detailed finite element analysis of each sample. The results obtained by analysis substantiate the observed dependence of stiffness on size. Classical elasticity theory does not acknowledge this size effect but more generalized elasticity theories do predict it. Micropolar elasticity theory has therefore been used to interpret the sample stiffness data and identify constitutive properties. Modulus values for the model materials have been quantified. Values of two additional constitutive properties, the characteristic length and the coupling number, which are present within micropolar elasticity but absent from its classic counterpart have also been determined. The dependence of these additional properties on void size has been investigated and characteristic length values compared to the length scales are inherent within the structure of the model materials.
  Highlights ► Measured the variation in stiffness with sample size for model void filled materials. ► Corroborated the measured results by detailed finite element analysis. ► Shown that the variations are consistent with micropolar elasticity theory. ► Quantified the micropolar constitutive properties for the materials. ► Determined how the constitutive properties vary with void size.
  
  PubDate: 2013-03-16T01:35:50Z
A Rankine–Timonshenko–Vlasov beam theory for anisotropic beams via an asymptotic strain energy transformation
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  A refined shear deformable beam theory is developed to analyze and design anisotropic beams via the mixed variational theorem (MVT). The developed theory is referred to as a Rankine–Timoshenko–Vlasov (RTV) beam theory since it is able to account for the torsional warping restraint as well as the shear deformation. The MVT is employed to systematically blend the asymptotic stress field and the intuitive displacement field, so that one can derive a simple yet accurate beam model. The asymptotic stress field is adopted from the finite element-based asymptotic expansion method, whereas the displacement field is intuitively assumed to have the form of a traditional shear deformable and torsional warping restrained beam model. The two fields are synthesized by a strain energy transformation via the MVT, which yields the RTV beam model whose degrees of freedom are the same as the traditional refined beam theories. The resulting generalized beam stiffness matrix is different from those traditional theories qualitatively as well as quantitatively. This leads to the accurate prediction of torsional rigidity, bimoment stiffness, transverse shear stiffness, and composite coupling stiffness. The thin-walled composite beams with closed and open cross-sections are taken as illustrative examples to demonstrate the accuracy and validity of the developed RTV theory.
  Highlights ► A new methodology to construct the composite beam theory is proposed. ► A strain energy transformation is conducted via the mixed variational theorem. ► The model includes both torsional warping restraint and shear deformation effects. ► Being asymptotically correct is important for non-classical behaviors.
  
  PubDate: 2013-03-08T01:39:03Z
Two-scale analytical solutions of multilayered composite rectangular plates with in-plane small periodic structure
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  We present a two-dimensional analytical solution of an orthotropic multilayered rectangular plate, which, in addition, has a small periodic structure along one in-plane direction. The two-scale asymptotic expansion method is first employed to develop a homogenized model of each individual layer in the plate. The laminated plate with homogenized layers is then analyzed exactly using the state-space approach. Two sets of approximate stresses (i.e. the homogenized model stresses and the zeroth-order two-scale model stresses) are presented analytically. Numerical examples are considered and comparison with the finite element simulation is made. It is shown that the two-scale model can give accurate predictions of the transverse normal stress even it varies sharply in a unit cell. It is also confirmed that the developed analytical solution can be used to investigate the effect of microstructure on the macroscopic behavior of the multilayered composite plate. This work presents an effort to take both advantages of the two-scale asymptotic expansion method and the state space method in the analyses of laminated composite structures with in-plane small periodicity.
  Highlights ► A two-scale method is employed first to develop a homogenized model. ► The homogenized model is then analyzed exactly using the state-space approach. ► It is the first effort to take both advantages of these two methods in a simulation. ► Numerical examples show the feasibility and correctness of our methodology.
  
  PubDate: 2013-03-04T01:39:25Z
Thermal vibration of magnetostrictive functionally graded material shells
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  The functionally graded material (FGM) shell with mounted magnetostrictive layer under thermal vibration was studied by using the generalized differential qradrature (GDQ) method. The FGM shell with/without negative velocity feedback of magnetostrictive position, with different power law index effects subjected to two edges lamped condition was analyzed. With velocity feedback and with suitable control gain value can reduce the amplitudes of displacement and shear stress into a smaller value. The magnetostrictive FGM shell is stable versus the Terfenol-D thickness for all values of FGM power law index. The magnetostrictive FGM shell can stand against the higher heating temperature of environment with some values of power law index.
  Highlights ► The FGM shell with mounted magnetostrictive layer under thermal vibration was studied by using GDQ method. ► With velocity feedback and suitable control gain value can reduce the amplitude of displacement into a smaller value. ► The magnetostrictive FGM shell is stable versus the Terfenol-D thickness for all values of FGM power law index.
  
  PubDate: 2013-03-04T01:39:25Z
Multiple cracks detection in a beam subjected to a moving load using wavelet analysis combined with factorial design
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  In this paper, a new method of multiple cracks detection in a simply supported beam subjected to a moving load along the beam based on Continuous Wavelet Transform (CWT) combined with factorial design is presented. Deflection of the beam when the moving load passes the mid span of the beam is considered. Peaks in the CWT coefficient of data using Gaussian4 Wavelet show Cracks' location. The value of CWT coefficient at the points of cracks assumed as Damage Index (DI). A technique for defining the velocity of moving load and normalizing the deflection introduced which makes the DI independent from beam material parameters. The important parameters which affect the damage index are found using factorial design. By introducing a novel multivariable curve fitting approach, an explicit expression for the DI is developed which shows effect of all important parameters clearly. Applying factorial design, it is shown that the DI of one crack does not depend on the size and location of other cracks in a multiple cracked beam. Hence, the obtained expression for the DI can be used to find the size of each crack independently. The proposed damage index can detect the crack depths of more than 5% of beam's height and can predict the size of crack even in the case of noisy data. The effect of 10% noise level on the beam having three cracks was introduced and is shown this noise level does not affect the procedure of damage detection introduced in this paper. Each crack is modeled as a rotational spring whose stiffness is obtained from fracture mechanics. The modal expansion theory is used to obtain the response of the beam due to moving load.
  Highlights ► CWT and factorial design were used for multiple crack detection in beams. ► Gaussian4 Wavelet shows Cracks' location. ► The value of CWT coefficient at the points of cracks is assumed as Damage Index (DI). ► Factorial design is used to find important parameters which affect the damage index. ► Crack depths of up to 5% of height can be detected even in the case of 10% noise.
  
  PubDate: 2013-03-04T01:39:25Z
Bending analysis of laminated sector plates with polar and rectilinear orthotropy
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  Bending of sector plates with both polar and rectilinear orthotropy is investigated using generalized differential quadrature (GDQ) method. The governing equations are written in polar coordinate system within the framework of the first-order shear deformation theory (FSDT). In polar orthotropic sector plates variation of thickness along radial direction due to moving out radial fibers, is considered. In rectilinear cases the variation of stiffness along circumferential direction due to variation of fiber angle with radial line, is considered. The governing equations are based on the FSDT which consists of thirteen first-order partial differential equations in terms of unknown displacements, rotations, forces and moments. Governing equations are discretized at whole domain grid points and boundary conditions are implemented exactly at boundary grid points using the GDQ method. Application of the GDQ technique to the governing equations, solution domain and boundary conditions leads to a system of algebraic equations. To compare the results of this study, the problems are also analyzed using commercial finite element software Abaqus. Various combinations of clamped, simply supported and free boundary conditions are implemented. It is found that the present method can analyze accurately sector plates with both polar and rectilinear orthotropy.
  Highlights ► Bending of sector plates with polar and rectilinear orthotropy is investigated. ► Radial thickness variation is considered for polar orthotropic sector plates. ► Circumferential stiffness variation is considered for rectilinear sector plates. ► The effects of thickness and stiffness variations are evaluated. ► Various boundary conditions, lay-ups and plate geometries are studied.
  
  PubDate: 2013-02-28T00:13:39Z
Non-local stiffness and damping models for shear-deformable beams
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  This paper presents the dynamics of a non-local Timoshenko beam. The key assumption involves modeling non-local effects as long-range volume forces and moments mutually exerted by non-adjacent beam segments, that contribute to the equilibrium of any beam segment along with the classical local stress resultants. Elastic and viscous long-range volume forces/moments are endowed in the model. They are built as linearly depending on the product of the volumes of the interacting beam segments and on generalized measures of their relative motion, based on the pure deformation modes of the beam. Attenuation functions governing the space decay of the non-local effects are introduced. Numerical results are presented for a variety of non-local parameters.
  Highlights ► The dynamics of a non-local Timoshenko beam is presented. ► Non-local effects are modeled as long-range volume forces/moments exchanged by non-adjacent beam segments. ► Elastic and viscous long-range volume forces/moments are considered, based on the pure deformation modes of the beam. ► Attenuation functions governing the space decay of the non-local effects are introduced. ► Numerical results are presented for a variety of non-local parameters.
  
  PubDate: 2013-02-28T00:13:39Z
Intensity of singularity in three-material joints under shear loading: Two-real singularities and power-logarithmic singularities
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  In the present study, the enriched finite element method is applied to analyze the intensity of singularity in 2D-dissimilar material joints described by 2-real singularities and power-logarithmic singularities. By using this method, the intensity of singularities can be directly evaluated and very refined meshes around the singular point are unnecessary. Eigenvalue and eigenvector analyses are applied to calculate the order of singularity and the asymptotic displacement fields on the enriched elements. Different mesh types (4-node and 8-node element) and different sizes of the enriched region are applied to improve the accuracy of the results. Furthermore, the models with various lengths and thicknesses are used to study an influence of geometry on the intensity of singularity. In conclusion, it is shown that the enriched finite element method can be used to determine the singular stress fields for both 2-real singularities and power-logarithmic singularities. An accuracy of the results can be improved by using higher order polynomial function for element shape function. Finally, a relationship between the intensity of singularity and geometry for three-material model with 2-real singularity is discussed.
  Highlights ► The enriched FEM is extended to solve power-logarithmic singularities. ► An accuracy of the results is improved by using higher order polynomial function. ► An influence of mesh size and enriched region on the intensity of singularity is considered. ► A relationship between the intensity of singularity and geometry is studied.
  
  PubDate: 2013-02-20T00:13:16Z
A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  A Kirchhoff micro-plate model is presented based on the modified strain gradient elasticity theory to capture size effects, in contrast with the classical plate theory. The analysis is general and can be reduced to the modified couple stress plate model or classical plate model once two or all material length scale parameters in the theory are set zero respectively. Governing equation and boundary conditions of an isotropic rectangular micro-plate are derived using minimum potential energy principle. Various boundary conditions including simply supported and clamped edges are covered by the analysis. The extended Kantorovich method (EKM) which is an accurate approximate closed-form solution is applied to solve the resulting sixth order boundary value problem. Application of EKM to the partial differential equation (PDE) yields two ordinary differential equations (ODEs) in the independent x and y coordinates. The resulted ODEs are solved in an iterative manner. Exact closed-form solutions are presented for both ODEs in all of the iteration. It is shown that the method provides accurate predictions with very fast convergence. Numerical results reveal that the differences between the deflection predicted by the modified strain gradient model, the couple stress model and the classical model are large when the plate thickness is small and comparable to the material length scale parameters. However, the differences decrease with increasing the plate thickness. Validation of the presented EKM solution shows good agreement with available literature.
  Highlights ► A Kirchhoff micro-plate model is presented based on the modified strain gradient elasticity. ► Governing equation and boundary conditions of a rectangular plate are derived by energy method. ► The extended Kantorovich method is used to solve the resulting sixth order boundary value problem.
  
  PubDate: 2013-02-20T00:13:16Z
A hollow osteon model for examining its poroelastic behaviors: Mathematically modeling an osteon with different boundary cases
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  A single osteon is modeled as a hollow poroelastic annular cylinder to examine its fluid pressure distribution and transport behavior. We propose an extension of the osteon model by considering four types of different boundary conditions that might be encountered in physiological environments or yet-to-be-developed laboratory testing procedures. This model links the external loads to the osteonal fluid pressure and velocity, which may have a significant stimulus to the mechanotransduction of bone remodeling signals. This model can also be used for analyzing other experiments performed on similarly shaped poroelastic specimens. The obtained analytical pressure and velocity solutions demonstrate the effects of the loading conditions and the material parameters. The results show the pore pressure and fluid velocity are both proportionate to the strain amplitude and the frequency. Nevertheless, the key loading role governing the poroelastic response of the osteon is strain rate. At the osteon scale, the pressure is also strongly affected by the material parameter of permeability variations whereas fluid velocity is not.
  Highlights ► We extend the osteon model by considering different boundary conditions. ► Both the pressure and velocity amplitudes are proportionate to frequency. ► Both the pressure and velocity amplitudes are proportionate to strain amplitude. ► The poroelastic behavior of the osteon is governed by the strain rate.
  
  PubDate: 2013-02-20T00:13:16Z
Editorial board
- Abstract: May–June 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 39
  
  PubDate: 2013-02-16T00:13:40Z
Multiscale thermopiezoelectric analysis of laminated plates with integrated piezoelectric fiber composites
- Abstract: July–August 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 40
  
  This study presents a comprehensive multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators. A detailed framework based on the asymptotic expansion homogenization method is developed to couple the microscale and macroscale field variables. The microscale fluctuations in temperature, mechanical displacement and electric potential are related to the macroscale temperature change, mechanical strain and electric fields through 43 distinct characteristic functions. The local thermal, mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using standard finite element techniques. The homogenized thermoelectroelastic properties of a representative material element are computed using the characteristic functions and the constituent material properties. The Eshelby–Stroh formalism is used to analytically solve the three-dimensional macroscopic equilibrium equations for thick and thin laminated piezoelectric plates with arbitrary boundary conditions at the edges. Interscale transfer operators emerging from the asymptotic expansion homogenization method relate the macroscale fields to the microscale heat flux, stress and electric displacement in the individual fibers and matrix. The present multiscale analysis procedure is demonstrated by considering two model problems. In the first problem, a simply-supported sandwich plate consisting of a piezoceramic fiber composite shear actuator embedded between two graphite/epoxy layers is studied. The second problem concerns a simply-supported graphite/epoxy substrate with piezoceramic fiber composite extension actuators attached to its top and bottom surfaces. In both model problems, the responses of the laminated plates under thermal and electrical loading conditions are examined. Results are presented for the homogenized material properties, macroscale deformation, macroscale average stresses and microscale stress distributions.
  Highlights ► We develop a multiscale framework for analyzing piezoelectric fiber composites. ► Macroscale temperatures, stresses, and electric fields are calculated analytically. ► Microscale fields are computed numerically using interscale transfer operators. ► Homogenized thermoelectroelastic properties compare well with analytical results. ► Differences in thermal expansion properties can result in high microscale stresses.
  
  PubDate: 2013-02-16T00:13:40Z
Stochastic study of a non-linear self-excited system with friction
- Abstract: Available online 11 January 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids
  
  This paper proposes two methods based on the Polynomial Chaos to carry out the stochastic study of a self-excited non-linear system with friction which is commonly used to represent brake-squeal phenomenon. These methods are illustrated using three uncertain configurations and validated using comparison with Monte Carlo simulation results. First, the stability of the static equilibrium point is examined by computing stochastic eigenvalues. Then, for unstable ranges of the equilibrium point, a constrained harmonic balance method is developed to determine subsequent limit cycles in the deterministic case; it is then adapted to the stochastic case. This demonstrates the effectiveness of the methods to fit complex eigenmodes as well as limit cycles dispersion with a good accuracy.
  Highlights ► A 2 dofs non-linear system with friction and 3 uncertain configurations are considered. ► 2 methods based on polynomial chaos and HBM are proposed. ► The stochastic eigenvalue problems are solved, investigating stability. ► Stochastic limit cycles on unstable ranges are evaluated.
  
  PubDate: 2013-01-19T09:10:01Z
Comparison of two homogenization methods using a damage model for a fibrous membrane, based on the fibers' fracture process at the microscale
- Abstract: May–June 2013
  Publication year: 2013
  Source:European Journal of Mechanics - A/Solids, Volume 39
  
  The objective of this paper is to evaluate two existing homogenization methods using a simple damage model for fibrous membrane and compare them. A macroscopic damage model of a fibrous membrane tissue based on the knowledge of the behavior and fracture process of a single fiber is constructed. Under some simplifying assumptions (linear behavior of the fibers, brittle fibers, constant angular distribution of the fibers), the evolution of fiber fracture is described by two macroscopic scalar variables; this enables the tissue's damage to be modeled without requiring a second discretization at the microscale. For the homogenization of the fibers contribution, an energetic method and a kinematic method are adapted and compared. Both lead to similar macroscopic behavior in the elastic phase, but the behavior differs in the fracture phase of the homogenized material. In the case of biological materials, the proposed law enables taking into account the often observed phenomena of crimping and damage of the fibers.
  Highlights ► A damage model for a fibrous membrane describes the evolution of anisotropy. ► The anisotropic macroscopic damage results from the failure of the brittle fibers. ► Two homogenization methods are adapted to the damage model and compared. ► The main difference between the two methods is observed on the less loaded direction. ► Fiber crimp and fiber damage can be included in the model.
  
  PubDate: 2012-12-18T09:12:08Z