Authors:Wen-An Jiang; Kun Liu; Zhao-Wang Xia; Li-Li Xia Pages: 2299 - 2306 Abstract: This paper investigates an algebraic structure and Poisson theory of single degree of freedom non-material volumes. The equations of motion are proposed in a contravariant algebraic form, and an algebraic product is determined. A consistent algebraic structure and a Lie algebra structure are proposed, and a proposition is obtained. The Poisson theory of the non-material volume is established, and five theorems are derived. Three examples are given to illustrate the application of the method. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2119-1 Issue No:Vol. 229, No. 6 (2018)

Authors:S. N. Korobeynikov; V. V. Alyokhin; A. V. Babichev Pages: 2343 - 2378 Abstract: Molecular mechanics/molecular dynamics (MM/MD) methods are widely used in computer simulations of deformation (including buckling, vibration, and fracture) of low-dimensional carbon nanostructures (single-layer graphene sheets (SLGSs), single-walled nanotubes, fullerenes, etc). In MM/MD simulations, the interactions between carbon atoms in these nanostructures are modeled using force fields (e.g., AIREBO, DREIDING, MM3/MM4). The objective of the present study is to fit the DREIDING force field parameters (see Mayo et al. J Phys Chem 94:8897–8909, 1990) to most closely reproduce the mechanical parameters of graphene (Young’s modulus, Poisson’s ratio, bending rigidity modulus, and intrinsic strength) known from experimental studies and quantum mechanics simulations since the standard set of the DREIDING force field parameters (see Mayo et al. 1990) leads to unsatisfactory values of the mechanical parameters of graphene. The values of these parameters are fitted using primitive unit cells of graphene acted upon by forces that reproduce the homogeneous deformation of this material in tension/compression, bending, and fracture. (Different sets of primitive unit cells are used for different types of deformation, taking into account the anisotropic properties of graphene in states close to failure.) The MM method is used to determine the dependence of the mechanical moduli of graphene (Young’s modulus, Poisson’s ratio, and bending rigidity modulus) on the scale factor. Computer simulation has shown that for large linear dimensions of SLGSs, the mechanical parameters of these sheets are close to those of graphene. In addition, computer simulation has shown that accounting for in-layer van der Waals forces has a small effect on the value of the mechanical moduli of graphene. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2115-5 Issue No:Vol. 229, No. 6 (2018)

Authors:D. P. Zhang; Y. J. Lei; S. Adhikari Pages: 2379 - 2392 Abstract: In this study, vibration characteristics of a piezoelectric nanobeam embedded in a viscoelastic medium are investigated based on nonlocal Euler–Bernoulli beam theory. In doing this, the governing equations of motion and boundary conditions for vibration analysis are first derived using Hamilton’s principle, where nonlocal effect, piezoelectric effect, flexoelectric effect, and viscoelastic medium are considered simultaneously. Subsequently, the transfer function method is employed to obtain the natural frequencies and corresponding mode shapes in closed form for the embedded piezoelectric nanobeam with arbitrary boundary conditions. The proposed mechanics model is validated by comparing the obtained results with those available in the literature, where good agreement is achieved. The effects of nonlocal parameter, boundary conditions, slenderness ratio, flexoelectric coefficient, and viscoelastic medium on vibration responses are also examined carefully for the embedded nanobeam. The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanobeam with flexoelectric effect, viscoelastic medium, and electrical loadings. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2116-4 Issue No:Vol. 229, No. 6 (2018)

Authors:Zhen Wu; Shiyin Liu; Huiwen Zhang; Xiaobo He; Junying Chen; Kai Yao Pages: 2393 - 2411 Abstract: The steady-state diagnostic and prognostic simulation for the Xiao Dongkemadi glacier (XD) of the Tibetan Plateau was performed with the thermo-mechanically-coupled-with-Full-Stokes code Elmer (http://www.csc.fi/elmer/). In this paper, some changes of glacial thermodynamic parameters caused by ice thickness and atmospheric temperature variation were simulated in view of different thickness. The purpose of this study was to fill the gap in analyzing the ice dynamic characteristic of a polar continental glacier. The diagnostic simulation revealed the following conclusions: (1) when the thickness change was small, surface velocity, ice temperature, and deviation stress variation in the bedrock showed a tendency to change with thickness, and when the terrain was gentle, the thickness variation dominated the ice velocity. (2) The ice temperature of the bedrock was high in the whole profile and reached the pressure melting point in the terminus, and it was easy to slide at the bottom, which was consistent with the measured ground penetrating radar data near the terminus. (3) The static friction forces decrease with thickness, and they showed a complex nonlinear relationship, which revealed that the deviation stress in the bottom was influenced by thickness and ice temperature at the bedrock. The prognostic simulating from 2007 to 2047 presented: (1) The simulation forecasted a shrinkage of nearly 600 m in the terminus and the longitudinal section, and wound up diminished by nearly 25% by the end of 2047; (2) the change of thickness was small at the region between 5650 and 5700 m.a.s.l, which might be related to lower atmospheric temperature; (3) thickness dominated the deviation stress ( \(\sigma _{xx}\) and \(\sigma _{xz}\) ) in the bottom, and the impact of the terrain was little higher compared to deviation stress ( \(\sigma _{xx}\) ). In other words, the glacial thickness dominated the glacial force and movement to a great extent and the low temperature at high altitude reduced the XD’s sensitivity facing future climate warming. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2112-8 Issue No:Vol. 229, No. 6 (2018)

Authors:Eman M. Hussein Pages: 2431 - 2444 Abstract: This manuscript investigates the thermal stresses and temperatures in a porous plate hydrated with a liquid. The upper surface is taken to be impermeable, traction free and subjected to a thermal shock. The lower surface is laid on a rigid foundation. The effect of the porosity is analyzed through graphs. It is noticed that all functions for the two phases increase with the increasing porosity except for the stress and the displacement. The effect of time is analyzed through graphs. It is observed that the heat and elastic effects propagate with finite speeds. Comparison is made with a problem with the same configuration in the absence of fluid when the medium is not porous. It was found that the existence of the fluid decreases the temperature and the displacement, whereas opposite behavior is observed for the stress. PubDate: 2018-06-01 DOI: 10.1007/s00707-017-2106-y Issue No:Vol. 229, No. 6 (2018)

Authors:Andrea Burlon; Giuseppe Failla; Felice Arena Pages: 2445 - 2475 Abstract: This paper deals with the coupled bending–torsional vibrations of beams carrying an arbitrary number of viscoelastic dampers and attached masses. Exact closed analytical expressions are derived for the frequency response under harmonically varying, arbitrarily placed polynomial loads, making use of coupled bending–torsion theory including warping effects and taking advantage of generalized functions to model response discontinuities at the application points of dampers/masses. In this context, the exact dynamic Green’s functions of the beam are also obtained. The frequency response solutions are the basis to derive the exact dynamic stiffness matrix and load vector of a two-node coupled bending–torsional beam finite element with warping effects, which may include any number of dampers/masses. Remarkably, the size of the dynamic stiffness matrix and load vector is \(8\times 8\) and \(8\times 1\) , respectively, regardless of the number of dampers/masses and loads along the beam finite element. PubDate: 2018-06-01 DOI: 10.1007/s00707-017-2078-y Issue No:Vol. 229, No. 6 (2018)

Authors:Wei Tong Pages: 2495 - 2519 Abstract: For better modeling plane-stress anisotropic plasticity of steel sheets, a direct calibration method is proposed and detailed for establishing a positive and convex sixth-order homogeneous polynomial yield function with up to sixteen independent material constants. The calibration method incorporates parameter identification, convexity testing, and if needed, an adjustment of an initially calibrated but non-convex yield function toward a convex one. Some advantages of the calibration method include (i) a systematic solution of only linear equations for the sixteen material constants of a steel sheet with various degrees of planar anisotropy, (ii) a practical numerical implementation of the necessary and sufficient conditions for convexity certification of the calibrated or adjusted yield function, and (iii) an incremental procedure using a parameterized version of the initially calibrated and non-convex yield function that can always lead to an approximate sixth-order yield function with guaranteed convexity. Results of applying the proposed calibration method to successfully obtain convex sixth-order yield functions are presented for three steel sheets with experimental measurement inputs from various types and numbers per type of uniaxial and biaxial tension tests. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2113-7 Issue No:Vol. 229, No. 6 (2018)

Authors:Alexander Svetashkov; Nikolay Kupriyanov; Kayrat Manabaev Pages: 2539 - 2559 Abstract: The problem of structural design of polymeric and composite viscoelastic materials is currently of great interest. The development of new methods of calculation of the stress–strain state of viscoelastic solids is also a current mathematical problem, because when solving boundary value problems one needs to consider the full history of exposure to loads and temperature on the structure. The article seeks to build an iterative algorithm for calculating the stress–strain state of viscoelastic structures, enabling a complete separation of time and space variables, thereby making it possible to determine the stresses and displacements at any time without regard to the loading history. It presents a modified theoretical basis of the iterative algorithm and provides analytical solutions of variational problems based on which the measure of the rate of convergence of the iterative process is determined. It also presents the conditions for the separation of space and time variables. The formulation of the iterative algorithm, convergence rate estimates, numerical computation results, and comparisons with exact solutions are provided in the tension plate problem example. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2129-z Issue No:Vol. 229, No. 6 (2018)

Authors:Sheng Sang; Eric Sandgren; Ziping Wang Pages: 2561 - 2569 Abstract: In this paper, we propose and study a single-phase elastic metamaterial with periodic chiral local resonator, which is composed of cylindrical central core surrounded by evenly distributed ligaments and embedded in the matrix in a square lattice. Based on the analytical and numerical analysis, we prove that the translational resonance of the unit cell can lead to negative effective mass density, and the rotational resonance of it can produce negative effective modulus. They can also work together to generate double-negative effective material properties. The wave attenuation of elastic waves in this elastic metamaterial is also demonstrated, which is owing to the negative effective mass density. In addition, the damping of the base material is also considered in the simulation. We finally examine the existence of negative band, and this leads to the physics of negative refraction, which is induced by simultaneous translational and rotational resonance of the unit cell. Our work can serve as the theoretical foundation for the design of single-phase elastic metamaterials. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2127-1 Issue No:Vol. 229, No. 6 (2018)

Authors:S. I. Kundalwal; Vijay Choyal Pages: 2571 - 2584 Abstract: Molecular dynamics simulations with Adaptive Intermolecular Reactive Empirical Bond Order force fields were conducted to determine the transversely isotropic elastic properties of carbon nanotubes (CNTs) containing vacancies. This is achieved by imposing axial extension, twist, in-plane biaxial tension, and in-plane shear to the defective CNTs. The effects of vacancy concentrations, their position, and the diameter of armchair CNTs were taken into consideration. Current results reveal that vacancy defects affect (i) the axial Young’s and shear moduli of smaller-diameter CNTs more than the larger ones and decrease by 8 and 16% for 1 and 2% vacancy concentrations, respectively; (ii) the plane strain bulk and the in-plane shear moduli of the larger-diameter CNTs more profoundly, reduced by 33 and 45% for 1 and 2% vacancy concentrations, respectively; and (iii) the plane strain bulk and in-plane shear moduli among all the elastic coefficients. It is also revealed that the position of vacancies along the length of CNTs is the main influencing factor which governs the change in the properties of CNTs, especially for vacancy concentration of 1%. The current fundamental study highlights the important role played by vacancy defected CNTs in determining their mechanical behaviors as reinforcements in multifunctional nanocomposites. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2123-5 Issue No:Vol. 229, No. 6 (2018)

Authors:Guangsong Chen; Linfang Qian; Jia Ma; Yicheng Zhu Pages: 2597 - 2618 Abstract: This paper presents a smoothed FE-Meshfree (SFE-Meshfree) method for solving solid mechanics problems. The system stiffness matrix is calculated via a strain-smoothing technique with the composite shape function, which is based on the partition of unity-based method, combing the classical isoparametric quadrilateral function and radial-polynomial basis function. The corresponding Gauss integration in the element is replaced by line integration along the edges of the smoothing cells, so no derivatives of the composite shape functions are needed during the field gradient estimation process. Several numerical examples including an automobile mechanical component are employed to examine the presented method. Calculation results indicate that SFE-Meshfree can obtain a high convergence rate and accuracy without introducing additional degrees of freedom to the system. In addition, it is also more tolerant with respect to mesh distortion. The volumetric locking problem is also explored in this paper under a selective smoothing integration scheme. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2124-4 Issue No:Vol. 229, No. 6 (2018)

Authors:Rittirong Ariyatanapol; Y.P. Xiong; Huajiang Ouyang Pages: 2619 - 2629 Abstract: Considering both single and multiple time delays, partial pole assignment for stabilising asymmetric systems is exemplified by friction-induced vibration and aerodynamic flutter. The control strategy is a single-input state feedback including constant time delays in the feedback loop. An unobservability condition is considered to assign some poles while keeping others unchanged. The receptance method is applied to avoid modelling errors from evaluating mass, damping and stiffness matrices by the finite element method. The solution is formulated in linear equations which allow determination of control gains. The stability of the closed-loop system is analysed by evaluating the first few dominant poles and determining a critical time delay. The numerical study shows that the proposed method is capable of making partial pole assignment with time delays. Since many structures and systems with non-conservative forces can be represented by asymmetric systems, this approach is widely applicable for vibration control of engineering structures. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2118-2 Issue No:Vol. 229, No. 6 (2018)

Authors:Sheng Sang; Ziping Wang Pages: 2647 - 2655 Abstract: In this paper, an elastic metamaterial is proposed by integrating a two-dimensionally periodic honeycomb lattice and tetrachiral metamaterial inclusions for low-frequency wave applications. Plane wave propagation in infinite periodic cells is investigated through using Floquet–Bloch principles and the finite element method. Two separate negative pass bands induced by different mechanisms appear in the band structures of wave propagation in the proposed elastic metamaterial. The working mechanisms of those two negative pass bands are revealed though analyzing the eigenmodes of the unit cell and the dynamic effective material properties. Numerical examples validate the proposed model and show that negative refraction of elastic waves in the elastic metamaterial has been obtained. The design concept of this type of elastic may be of use for the design of broadband flat lenses for elastic wave focusing. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2128-0 Issue No:Vol. 229, No. 6 (2018)

Authors:Kourosh Hasanpour; Davoud Mirzaei Pages: 2657 - 2673 Abstract: This paper concerns a new and fast meshfree method for the linear coupled thermoelasticity problem. The resulting algorithm provides an attractive alternative to existing mesh-based and meshfree methods. Compared with mesh-based methods, the proposed technique inherits the advantages of meshfree methods allowing the use of scattered points instead of a predefined mesh. Compared with the existing meshfree methods, the proposed technique is truly meshless, requiring no background mesh for both trial and test spaces and, more importantly, numerical integrations are done over low-degree polynomials rather than complicated shape functions. In fact, this method mimics the known advantages of both meshless and finite element methods, where in the former triangulation is not required for approximation and in the latter the stiffness and mass matrices are set up by integration against simple polynomials. The numerical results of the present work concern the thermal and mechanical shocks in a finite domain considering classical coupled theory of thermoelasticity. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2122-6 Issue No:Vol. 229, No. 6 (2018)

Authors:H. Yazdani Sarvestani; A. H. Akbarzadeh; A. Mirabolghasemi Pages: 2675 - 2701 Abstract: Advances in multi-material 3D printing technologies have opened a new horizon for design and fabrication of architected multi-materials in multiple length scales from nano-/microscale to meso-/macroscales. In this study, we apply modified couple stress and first-order shear deformation theories for a size-dependent structural analysis of 3D printable functionally graded (FG) doubly-curved panels where their microarchitecture can be engineered to improve their structural performance. This non-classical model incorporates the microstructure-dependent size effects for the structural performance through the introduction of a length scale in the kinematics of deformation. The volume fraction of matrix in the dual-phase (inclusion and matrix) FG size-dependent panels varies continuously through the thickness. The microarchitecture of inclusion and matrix in FG panels is engineered to show its effect on the structural responses. We implement the standard mechanics homogenization technique via finite element simulation to accurately predict the effective mechanical properties of FG materials for different topologies of engineered microarchitecture to show the significance of selecting appropriate micromechanical modeling for analyzing FG structures. Governing equations derived by variational Hamilton’s principle are solved by applying the Galerkin method for different sets of boundary conditions. We investigate the effects of material length scale, material composition, heterogeneous material distribution, particulate topology, length-to-thickness ratio, and panel curvature on the structural performance. It is found that the fundamental frequencies of size-dependent two-phase FG doubly-curved panels with square-shape inclusions are higher than for those with other topologies, which sheds lights on the engineering of the inclusion shape in advanced architected materials to optimize their structural performance. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2120-8 Issue No:Vol. 229, No. 6 (2018)

Authors:Ileana Corbi; Ottavia Corbi Abstract: In this paper, the problem of identifying the optimal amount of composite reinforcement for a given masonry structure and its optimal dislocation over the structure is addressed through the set-up of a topology optimum problem. The topological optimization theory was originally developed for searching the equilibrium path of 3D solids under sets of applied loads. The main outcome of the topology process consisted of the identification of the optimal shape of the structure resisting the given active forces. The observation of an extreme variation and a high degree of arbitrariness in selecting the refurbishment shapes in technical and experimental tests executed on masonry structures gave birth to the original idea developed by the authors of applying the topology optimization’s fundamentals to the field of FRP and FRCM refurbishment of masonry structures. The idea is essentially based on the principle that a tensile composite strip/sheet is required to work only in the areas of the masonry solid where the tensile stress cannot be avoided. If no tensile stress arises in a region of the structure, then the adoption of the reinforcement is not needed in that area since the intervention would certainly be uneconomic in this case, and it might also produce some damage to the global stability of the structure. PubDate: 2018-06-09 DOI: 10.1007/s00707-018-2184-5

Authors:Mahdi Fakoor; Maryam S. Shokrollahi Abstract: In this paper a new criterion for fracture investigation of orthotropic materials with cracks under mixed mode I/II loading is presented. In this fracture criterion, orthotropic material will be considered as a reinforced isotropic material. It is supposed that the crack will grow in the matrix of the orthotropic material. A new definition named here as “isotropic–orthotropic stress reduction factor” (IO-SRF) is utilized to consider the effects of the fracture process zone by a macro-mechanics approach. Also, the stress reduction factors will present a valuable relationship between the orthotropic and isotropic fracture toughness. Experimental and finite element methods will be introduced for computing the stress reduction factors. The SRFs are calculated for samples of glass–epoxy as an orthotropic material and samples of epoxy as a related isotropic one. Experimental tests under mixed mode I/II are performed on glass–epoxy composite samples to evaluate the validity of the presented mixed mode fracture criterion. The results of experimental tests on composite samples show a good agreement with the results of the presented criterion. Thus, the proposed criterion could be utilized as an efficient criterion for investigating the fracture of orthotropic materials under mixed mode I/II loading. PubDate: 2018-06-09 DOI: 10.1007/s00707-018-2132-4

Authors:Aleksandar S. Okuka; Dušan Zorica Abstract: The approach of viscoelastic body constitutive equation fractionalization using rheological representation of the classical Burgers model and considering the Scott–Blair (fractional) elements instead of the dash-pot elements is adopted. The obtained fractional Burgers model is further generalized by considering arbitrary model parameters: multiplicative constants and orders of fractional differentiation. Thermodynamical consistency of the fractional Burgers model is analyzed, resulting in formulation of eight thermodynamically consistent fractional Burgers models. PubDate: 2018-06-09 DOI: 10.1007/s00707-018-2198-z

Authors:J. Reboul; G. Vadillo Abstract: In this paper, the classical Gurson model for ductile porous media is extended for strain-rate-dependent materials. Based on micromechanical considerations, approximate closed-form macroscopic behavior equations are derived to describe the viscous response of a ductile metallic material. To this end, the analysis of the expansion of a long cylindrical void in an ideally plastic solid introduced by McClintock (J Appl Mech 35:363, 1968) is revisited. The classical Gurson yield locus has been modified to explicitly take into account the strain rate sensitivity parameter for strain rate power-law solids. Two macroscopic approaches are proposed in this work. Both models use the first term of a Taylor series expansion to approximate integrals to polynomial functions. The first proposed closed-form approach is analytically more tractable than the second one. The second approach is more accurate. In order to compare the proposed approximate Gurson-type macroscopic functions with the behavior of the original Gurson yield locus, numerical finite element analyses for cylindrical cells have been conducted for a wide range of porosities, triaxialities, and strain rate sensitivity parameters. The results presented evidence that, for large values of the rate sensitivity parameters, the proposed extended Gurson-type models have the important quality to better predict the behavior of rate sensitive materials than the classical one. They also provide simpler and accurate alternatives to more traditional viscoplastic models. PubDate: 2018-06-05 DOI: 10.1007/s00707-018-2189-0

Authors:Colin Rogers; Giuseppe Saccomandi; Luigi Vergori Abstract: A nonlinear elastodynamic system is investigated which is descriptive of transverse wave propagation in an isotropic, incompressible, hyperelastic material subject to body forces associated with a nonlinear substrate potential. Notably, by introducing an appropriate ansatz, both cnoidal and gausson-type exact solutions are isolated. PubDate: 2018-06-01 DOI: 10.1007/s00707-018-2187-2