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• The CPFEM of TA15 matrix during hot rolling and tensile was built. • The mechanism of orientation evolution of β-phase was studied by CPFEM. • The finite element model of TA15/TiBw composites during tensile was built. • The mechanical properties caused by matrix texture and TiBw was analyzed. An in-depth understanding of the crystal orientation evolution during hot rolling of TiB whisker (TiBw) /TA15 composites and the anisotropy of the as-rolled plates can help fully utilize the material properties. In this paper, the crystal plasticity finite element models of high-temperature (HT) β-phase and room-temperature (RT) α-phase were constructed from electron backscattering diffraction data. Based on this, the orientation evolution during hot rolling in the single-phase region and the effects of the matrix texture on the mechanical properties of the as-rolled plates were analyzed. The effect of TiBw on the anisotropy was studied by the composites finite element model. Results showed that the α-fiber texture of the β-phase was formed during HT rolling. This texture was converted to the T-texture of the α-phase at RT during cooling according to the Burgers orientation relationships. The TiBw had little effect on the matrix texture composition. The TiBw and matrix texture caused the matrix to have higher strength along the rolling direction and the transverse direction, respectively. The matrix texture dominated the difference in mechanical properties because its effect exceeded that of TiBw. The effect of the matrix on the mechanical properties was caused by the Schmid factors (SFs) and the critical resolved shear stress (CRSS) of the slip system together. The slip mode was influenced by SFs determined by the angular relationship between the crystal orientation and the loading direction. The CRSS of the activated slip system determined the yield strength. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with Trefftz discretizations of the time-dependent Maxwell equations in anisotropic media in three-dimensional domains. We propose a class of space–time Trefftz DG methods, which include the Trefftz variational formulation from Egger et al. (2015). We prove the error estimates of the approximate solutions with respect to the meshwidth and the condition number of the coefficient matrices. Furthermore, we propose the global Trefftz DG method combined with local DG methods to solve the time-dependent linear nonhomogeneous Maxwell equations in anisotropic media. The numerical results verify the validity of the theoretical results, and show that the resulting approximate solutions possess high accuracy. [ABSTRACT FROM AUTHOR]

• Performance of 3D printing ceramic core can meet the casting requirements of single crystal superalloy blade, and is a potential technology for the preparation of complex ceramic core structure. • The 3D printed ceramic core had a typical layered structure, and the pore diameter was small. Net-like ZrO 2 was formed around the SiO 2 particles, which promoted the formation of ZrSiO 4 , quartz and cristobalite in the sintering process. • Potential improvement direction of stereolithography 3D printed ceramic cores was proposed based on the hot injection process. • Researching 3D printing core technology based on the traditional hot injection process provides an effective new idea for promoting the industrial application of 3D printing core technology. With the improvement of aero-engine performance, the preparation of hollow blades of single-crystal superalloys with complex inner cavity cooling structures is becoming increasingly urgent. The ceramic core is the key intermediate part of the preparation and has attracted wide attention. To meet this challenge, new technologies that can make up for the defects of long periods and high costs of fabricating complex structural cores by traditional hot injection technology are needed. Vat photopolymerization 3D printing ceramic technology has been applied to the core field to realize the rapid preparation of complex structural cores. However, the industrial application of this technology still needs further research and improvement. Herein, ceramic cores were prepared using traditional hot injection and vat photopolymerization 3D printing techniques using fused silica, nano-ZrO 2 , and Al 2 O 3 powders as starting materials. The 3D printed ceramic core has a typical layered structure with a small pore size and low porosity. Because of the layered structure, the pore area is larger than that of the hot injection ceramic core, the leaching performance has little effect (0.0277 g/min for 3D printing cores, 0.298 g/min for hot injection cores). In the X and Y directions, the sintering shrinkage is low (2.7%), but in the Z direction, the shrinkage is large (4.7%). The fracture occurs when the inner layer crack expands and connects with the interlayer crack, forming a stepped fracture in the 3D-printed cores. The bending strength of the 3D printed core at high temperature (1500 °C) is 17.3 MPa. These analyses show that the performance of vat photopolymerization 3D-printed ceramic cores can meet the casting requirements of single crystal superalloy blades, which is a potential technology for the preparation of complex structure ceramic cores. The research mode of 3D printing core technology based on the traditional hot injection process provides an effective new idea for promoting the industrial application of 3D printing core technology. [Display omitted] [ABSTRACT FROM AUTHOR]

A unified expression for the generalized two-dimensional linear anisotropic elastic, piezoelectric, and magneto-electro-elastic (MEE) solids is established to simplify the connection between these three different kinds of materials. Here, the two-dimensional assumption includes the most general cases that in-plane and anti-plane deformations are allowed to couple each other. Based upon this unified expression, in this paper a recently developed boundary element method (BEM) for contact of two anisotropic elastic bodies is extended to solve the problems of multibody contact in which the bodies can be any combination of anisotropic elastic, piezoelectric and MEE solids. When a special case of contact between multiple rigid punches and an anisotropic elastic, piezoelectric or MEE half-plane is considered, further reduction can be made by introducing three degrees of freedom (two rigid body translations and one rigid body rotation) for each punch. With this consideration, no meshes are required on the rigid punches. The usual contact modes of separation, stick, and slip all include the situation of conductor and insulator if any one of the multibody is piezoelectric or MEE. In other words, in this paper we successfully develop two BEMs to solve the generalized two-dimensional problems of multibody contact. One is for the general cases whose bodies can be any combination of anisotropic elastic, piezoelectric and MEE solids, and the other is for the special cases of multiple rigid punches indenting on an anisotropic elastic, piezoelectric or MEE half-plane. [ABSTRACT FROM AUTHOR]

• We present a semi-analytical modeling approach for frictional contact of two dissimilar deformable anisotropic bodies. • Contact bodies can be anisotropic elastic, piezoelectric and magneto-electro-elastic materials. • Contact surface is either electric insulating or conducting and either magnetic insulating or conducting. • Influence matrix is calculated analytically, establishing the effectiveness of the semi-analytical method. • Correctness and versatility are illustrated, and the important parameters are studied. In this paper, we utilize the surface Green's function of a magneto-electro-elastic (MEE) half-plane as a general analytical kernel to develop a semi-analytical method (SAM). This SAM is designed to solve the two-dimensional contact problems of two dissimilar deformable anisotropic MEE bodies. Using the surface Green's function, the associated influence matrices in SAM can be obtained in a closed mathematical form and then computed analytically, offering significant benefits in terms of computational efficiency and accuracy. This method can be applied to general contact problems where the contact surface is frictional sliding and subjected to four different electric and magnetic conditions. By assuming the elastic and piezoelectric materials as uncoupled MEE materials, the method can also be applied to contact problems in which anisotropic elastic and piezoelectric materials are involved. To demonstrate the accuracy and applicability of the proposed SAM, four different numerical examples are provided, and their results are compared with those obtained by using other approaches, such as analytical solutions and the previous SAM in the literature. Through the numerical results, parametric studies are also performed, allowing us to explore the influences of material properties, loadings, frictional coefficient, and contact surface profile on mechanical/electrical/magnetic contact behaviors. [ABSTRACT FROM AUTHOR]

Scaling-laws are ubiquitous as universal physical principles in physics, biological systems, and human behavior. The scaling-law rheological responses of viscoelastic and plastic deformations and rate-dependent softening and stiffening during dynamic loading are remarkable characteristics of living cells and cell-like materials; however, the underlying mechanisms remain poorly understood. Here, we first propose a cellular structural model with 3-dimensional anisotropic discrete and plastic cytoskeletal networks to study the scaling-law rheological responses of cells. Besides the scaling-law invariance observed in cellular plastic deformation and viscoelastic deformation under large force ranges, there is evidence of scaling-law variance under relatively small force ranges. We develop a minimal mechanical model to elucidate the origins of scaling-law variance and invariance of cellular viscoelastic and plastic deformations. Interestingly, we find that cell materials can transition from fluid to solid over time and from elasticity to plasticity with increasing force. Furthermore, it is shown that the heterogeneity of three-dimensional cytoskeletal network dominates the anisotropic viscoplastic behavior of cells. We show that the stress-strain curves of cells with plastic cytoskeletons can be collapsed onto a single master curve of cells with elastic cytoskeletons. Moreover, we discover and derive a novel scaling-law Δ F ∼ v 0 α wherein the extent of force relaxation on cells during cyclical mechanical stimuli follows the same power-law dependence on the loading rate, as creep compliance on time. Our findings provide evidence that structure-based simulation and theoretical models can naturally capture the scaling-law invariance and variance of cellular deformations, in agreement with many experimental findings. [ABSTRACT FROM AUTHOR]

• The typical texture in wrought Mg alloy and its effect on mechanical properties. • Texture evolution during alloying or processing. • The mechanism of texture weakening. The crystallographic orientations are generally non-random in wrought Mg alloy, which will lead to their macroscopic physical properties to be anisotropic. Understanding the texture evolution in processing of Mg alloy billets and its effect on mechanical properties is therefore an important project for all scientists and engineers in material area. This paper is concerned with the description of texture, with the mechanisms of texture evolution and with the interrelationships between texture and mechanical properties in Mg alloy. It is a full review of understanding of the basic mechanism on texture evolution, of texture altering by alloying or processing, and of the mechanism of texture weakening. Moreover, it provides theories necessary and available techniques to develop high-performance Mg wrought with optimized texture in the field. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to propose a novel efficient design optimization technique based on the operational quadrature boundary element method (OQBEM) for a simulation study on the material distribution and influence of rotation on the optimal design of rotating anisotropic viscoelastic porous permeable structures. An implicit differentiation method was developed to calculate the design sensitivities of displacements and pore pressure with respect to design variables and the effects of rotation on these sensitivities are also discussed. The optimization problem is solved using the Moving Asymptotes Method (MAM) which requires the calculation of the sensitivities for objective function and constraints by adjoint variable method. The optimum shape design of an elliptical sandwich structure is used as the numerical example to verify the validity and accuracy of the proposed technique. [ABSTRACT FROM AUTHOR]

Abstract This paper documents the first attempt to apply the generalized finite difference method (GFDM), a recently-developed meshless method, for the numerical solution of problems with cracks in general anisotropic materials. To solve the resulting second-order elliptic partial differential equations with mixed boundary conditions, the explicit formulae for the partial derivatives of unknown functions in the equations are derived by using the Taylor series expansions combining with the moving-least squares approximation in this meshless GFD method. To deal with the strong discontinuous crack-faces, some special treatments are applied to modify this GFDM. The node distributions are locally refined in the vicinity of the crack-tips. By dividing the crack domain into two parts, the sub-domain method is also used for comparing with the single-domain method. The direct displacement extrapolation method, the path-independent J -integral and the interaction integral methods are, respectively, used to compute the stress intensity factors and compared. Finally, some classical crack examples are presented to show the effectiveness and accuracy of the proposed meshless method for crack problems. [ABSTRACT FROM AUTHOR]

Protein microtubules (MTs) are one of the important intercellular components and have a vital role in the stability and strength of the cells. Due to applied external loads, protein microtubules may be involved buckling phenomenon. Due to impact of protein microtubules in cell reactions, it is important to determine their critical buckling load. Considering nature of protein microtubules, various parameters are effective on microtubules buckling. The small size of microtubules and also lack of uniformity of MTs properties in different directions caused the necessity of accuracy in the analysis of these bio-structure. In fact, microtubules must be considered as a size dependent cylinder, which behave as an orthotropic material. Hence, in the present work using first-order shear deformation model (FSDT), the buckling equations of anisotropic MTs are derived based on new modified couple stress theory (NMCST). After solving the stability equations, the influences of various parameters are measured on the MTs critical buckling load. [ABSTRACT FROM AUTHOR]

A common numerical task is to represent functions which are highly spatially anisotropic, and to solve differential equations related to these functions. One way such anisotropy arises is that information transfer along one spatial direction is much faster than in others. In this situation, the derivative of the function is small in the local direction of a vector field B . In order to define a discrete representation, a set of surfaces M i indexed by an integer i are chosen such that mapping along the field B induces a one-to-one relation between the points on surface M i to those on M i + 1 . For simple cases M i may be surfaces of constant coordinate value. On each surface M i , a function description is constructed using basis functions defined on a regular structured mesh. The definition of each basis function is extended from the surface M along the lines of the field B by multiplying it by a smooth compact support function whose argument increases with distance along B . Function values are evaluated by summing contributions associated with each surface M i . This does not require any special connectivity of the meshes used in the neighbouring surfaces M , which substantially simplifies the meshing problem compared to attempting to find a space filling anisotropic mesh. We explore the numerical properties of the scheme, and show that it can be used to efficiently solve differential equations for certain anisotropic problems. [ABSTRACT FROM AUTHOR]

A method for representing highly anisotropic fields is presented, based on a partially meshfree Galerkin formulation. A mapping function is used to provide information about the local direction of the anisotropy, with one of the global coordinates chosen to parameterize the 'parallel' position along the mapping in a one-to-one manner. Standard unstructured finite element meshes are used on planes of constant parallel coordinate to represent the necessary small-scale variations perpendicular to the mapping direction, with large spacings then possible between these planes because of the large-scale variations along the mapping. This greatly reduces the number of degrees of freedom required to represent fields in this space and the associated computational cost of simulations involving such fields. No mesh connectivity is defined between planes, and field aligned basis functions are constructed using the mapping function to extend the standard finite element basis into the full domain. Integration of the basis has been addressed with reference to methods developed for fully meshfree methods, and the scheme (as well as other similar element-free Galerkin schemes) is shown to be locally conservative under certain conditions. Robust convergence of several test problems is demonstrated. • Alignment of basis functions to anisotropy reduces degrees of freedom required. • Mapping function encodes potentially complex directional variation of anisotropy. • Meshfree aspects obviate difficult/impossible generation of field-aligned meshes. • Local point-wise flux conservation can be achieved for any similar Galerkin scheme. • Variationally consistent quadrature reweighting maintains conservation property. [ABSTRACT FROM AUTHOR]

The paper presents a general boundary element approach for analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids. Dual boundary integral equations are derived, which kernels are explicitly written. These equations do not contain volume integrals in the absence of distributed body heat and extended body forces, which is advantageous comparing to the existing approaches. The issues on the boundary element solution of these equations are discussed in details. The efficient numerical evaluation of kernels based on the trapezoid rule is proposed. Modified Kutt's quadrature with Chebyshev nodes is derived for integration of singular and hypersingular integrals. Nonlinear polynomial mappings are adopted for smoothing the integrand at the crack front, which is advantageous for accurate evaluation of field intensity factors. Special shape functions are introduced, which account for a square-root singularity of extended stress and heat flux at the crack front. The issues on numerical determination of field intensity factors are discussed. Several numerical examples are presented, which show the efficiency (low computational time and high precision) of the proposed boundary element formulation. [ABSTRACT FROM AUTHOR]

Based on the modified couple-stress theory, the size-dependent behavior of the functionally graded anisotropic elastic composites is analytically investigated when the load is applied on the top surface of the composite plate. The functionally graded material is assumed to be exponential in the thickness direction of the plate. By expanding the solutions of the displacements in terms of the two-dimensional Fourier series, the final governing equations are reduced to an eigenvalue and eigenvector problem. The exact solutions of the elastic fields with the modified couple-stress effect are derived under two kinds of boundary conditions. The classical elastic solutions are reduced from the present solutions as a special case. Numerical examples show the effect of the functional gradient factor and the material length-scale on the elastic fields along the thickness direction of the plate. Some important features observed in this paper could be useful in designing the functionally graded laminated composites with size-dependency. [ABSTRACT FROM AUTHOR]

We have implemented tetrahedral anisotropic mesh adaptation using the local operations of coarsening, swapping, refinement and smoothing in MATLAB without the use of any for- N loops, i.e. the script is fully vectorised. In the process of doing so, we have made three observations related to details of the implementation: 1. restricting refinement to a single edge split per element not only simplifies the code, it also improves mesh quality, 2. face to edge swapping is unnecessary, and 3. optimising for the Vassilevski functional tends to give a little higher value for the mean condition number functional than optimising for the condition number functional directly. These observations have been made for a uniform and a radial shock metric field, both starting from a structured mesh in a cube. Finally, we compare two coarsening techniques and demonstrate the importance of applying smoothing in the mesh adaptation loop. The results pertain to a unit cube geometry, but we also show the effect of corners and edges by applying the implementation in a spherical geometry. Program summary Program title: trullekrul v0.1.0 Catalogue identifier: AEZC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEZC_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: New style BSD license No. of lines in distributed program, including test data, etc.: 8395 No. of bytes in distributed program, including test data, etc.: 92021 Distribution format: tar.gz Programming language: MATLAB/GNU Octave. Computer: Single core desktops. Operating system: Linux/Windows/Mac. RAM: Variable, from megabytes to gigabytes Classification: 4.2, 4.3, 4.12, 4.14. Nature of problem: Adaptation of tetrahedral meshes to metric fields. Solution method: Local operations, colouring and APL vectorised code. Restrictions: Region IDs/internal boundaries are not supported and 3D adaptation with 1M elements requires ≈ 4 GB memory. Unusual features: Vectorised script implementation, signed distance functions, selection of refinement and coarsening techniques. Running time: 2D problems solve in seconds, but 3D problems can take up to an hour without running out of memory. [ABSTRACT FROM AUTHOR]

The paper derives Somigliana type boundary integral equations for 3D thermomagnetoelectroelasticity of anisotropic solids. In the absence of distributed volume heat and body forces these equations contain only boundary integrals. Besides all of the obtained terms of integral equations are to be calculated in the real domain, which is advantageous to the known equations that can contain volume integrals or whose terms should be calculated in the mapped temperature domain. All kernels of the derived integral equations and the 3D thermomagnetoelectroelastic Green׳s function for a point heat are obtained explicitly based on the Radon transform technique. Verification of the obtained equations and fundamental solutions is provided. [ABSTRACT FROM AUTHOR]

This paper utilizes the Stroh formalism and the complex variable approach to derive the integral formulae and boundary integral equations of anisotropic thermoelectroelasticity for a bimaterial solid with Kapitza-type interface. Obtained integral formulae and boundary integral equations do not contain domain integrals, thus, the boundary element approach based on them does not require any additional procedures accounting for the stationary temperature field acting in the solid. All kernels of the boundary integral equations are written explicitly in a closed form. Verification for limiting values of thermal resistance of the interface is provided. Obtained boundary integral equations are incorporated into the boundary element analysis procedure. Several problems are considered, which shows the influence of thermal resistance of the bimaterial interface on fields’ intensity at the tips of electrically permeable and impermeable cracks. [ABSTRACT FROM AUTHOR]

In this paper, the formulation of nonlinear thermomechanics and electrodynamics of deformable materials proposed by Eringen and Maugin (1990) is restructured using the thermomechanical formulation of Green and Naghdi (1977, 1978). Constitutive equations for thermoelastic solids are typically proposed using Lagrangian forms of deformation variables. Consequently, previous developments of constitutive equations for thermoelastic electrodynamic materials proposed Lagrangian forms of electrodynamic quantities. In contrast, here, an Eulerian formulation is proposed which naturally unifies the constitutive modeling. In particular, the formulation does not use electrodynamic body force or body couple terms and the nonlinear constitutive equations for thermomechanical and electrodynamic variables are determined by derivatives of a single Helmholtz free energy function. Also, the constitutive equations for electrodynamic contributions to the stress tensor, the polarization and magnetization vectors depend naturally on the specific functional form of the Helmholtz free energy and need not be proposed independently. [ABSTRACT FROM AUTHOR]

The distance r between the source point and the field point is very short when the boundary element method is used to calculate the boundary quantities in the coating domain, which is very thin with respect to the substrate. The nearly singular integrals will occur during the process of numerical calculation of the boundary integral equations when the distance r is approaching to zero. The calculation difficulty of nearly singular integrals has seriously hindered the application of the boundary element method to the analysis of the physical quantities in the coating-structures. Herein, the analytical formulations for the nearly singular integrals in potential boundary integral equations developed by the authors before are generalized to the multi-domain system. This multi-domain boundary element method, in which the nearly singular integrals have been cracked, is introduced to analyze the temperature field in anisotropic coating-structures. The numerical examples demonstrate that the present method can model the temperature field in the coating-structure with much thinner coating in contrast with the conventional boundary element method. For the cases there are no analytical solutions available, the solutions from the finite element method are given out as the referenced ones. The temperature fields obtained by the present method can approach to the finite element solutions perfectly when the coating is very thin. The present method is versatile for the temperature analysis of the isotropic, orthotropic and anisotropic coating-structures. [ABSTRACT FROM AUTHOR]

A new yield criterion is proposed for transversely isotropic solid foams. Its derivation is based on the hypothesis that the yielding in foams is driven by the total strain energy density, rather than a completely phenomenological approach. This allows defining the yield surface with minimal number of parameters and does not require complex experiments. The general framework used leads to the introduction of new scalar measures of stress and strain (characteristic stress and strain) for transversely isotropic foams. Furthermore, the central hypothesis that the total strain energy density drives yielding in foams ascribes to the characteristic stress an analogous role of von Mises stress in metal plasticity. Unlike the overwhelming majority of yield models in literature the proposed model recognizes the tension–compression difference in yield behavior of foams through a linear mean stress term. Predictions of the proposed yield model are in excellent agreement with the results of uniaxial, biaxial and triaxial FE analyses implemented on both isotropic and transversely isotropic Kelvin foam models. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on the 2D boundary integral equations, Green׳s functions and boundary element method for thermoelectroelastic bimaterials containing cracks and thin inclusions. Based on the extended Stroh formalism, complex variable approach and the Cauchy integral formula, the paper derives integral formulae for the Stroh complex functions, and Somigliana type integral identities for 2D thermoelectroelastic bimaterial. The kernels arising in the integral formulae are obtained explicitly and in a closed-form. It is proved that these kernels are fundamental solutions for a line extended force and a line heat. The far-field mechanical, electric and thermal load and internal volume load are accounted for in the obtained integral formulae. The latter allow to derive boundary integral equations for a bimaterial containing holes, cracks and thin inclusions, and to develop the corresponding boundary element approach. Special tip boundary elements used in the analysis allow accurate determination of the stress and electric displacement intensity factors for cracks and thin deformable inclusions. Several numerical examples are considered that show the validity and efficiency of the developed boundary element approach in the analysis of defective thermoelectroelastic anisotropic bimaterials. [ABSTRACT FROM AUTHOR]

Kinematic boundary condition is usually used when dealing with transient free-surface flow problems in isotropic media. When dealing with anisotropic problems, a transformation can transform the anisotropic media to an equivalent isotropic media for seepage analysis, but the kinematic boundary condition cannot be used directly in the transformed media. A generalization of the kinematic boundary condition along any arbitrary direction is derived for use in the transformed domain for general three-dimensional anisotropic problems. A boundary element method for solving transient free-surface seepage problems is developed and the treatment of the proposed kinematic boundary condition in the boundary element method is given. Three examples have been solved to show the reliability and flexibility of the model. Examples are verified with some available experimental and numerical cases to show the accuracy of the model for predicting the phreatic surface and it is shown that anisotropy has a very important and non-neglecting effect in the behavior and the shape of phreatic surface. [ABSTRACT FROM AUTHOR]

Abstract: A weakly singular symmetric Galerkin boundary element method (SGBEM) is developed for analysis of fractures in two-dimensional multi-field media. Specialization for the cases of anisotropic linear elasticity, piezoelectricity and magnetoelectroelasticity is considered. The basis for the method is a pair of weak-form integral equations for ‘generalized’ displacement and traction that involve only (at most) weakly singular kernels of order . Standard elements are employed everywhere except at the crack tips. A special crack-tip element is developed to properly model the asymptotic behavior of the relative crack-face displacements. Extra degrees of freedom at the tip node are incorporated in the crack-tip element so that the ‘generalized’ stress intensity factors are directly obtained from the solution to the system of discretized equations. Various examples for cracks in both infinite and finite domains are examined. Highly accurate results are obtained with relatively coarse meshes. [Copyright &y& Elsevier]

Abstract: The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelectroelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and Stroh orthogonality relations to obtain the integral formulae for the Stroh complex functions, which are piecewise-analytic in the complex half-plane with holes and opened mathematical cuts. Further application of the Stroh formalism allows derivation of the Somigliana type integral formulae and boundary integral equations for a thermoelectroelastic half-space. The kernels of these equations correspond to the fundamental solutions of heat transfer, electroelasticity and thermoelectroelasticity for a half-space. It is shown that the difference between the obtained fundamental solution of thermoelectroelasticity and those presented in literature is due to the fact, that present solution additionally accounts for extended displacement and stress continuity conditions, thus, it is physically correct. Obtained integral equations are introduced into the boundary element approach. Numerical examples validate derived boundary integral equations, show their efficiency and accuracy. [Copyright &y& Elsevier]

Purpose – This work seeks to analyze the heat transfer phenomena of anisotropic thermal conductivity fabrics containing electric conductive yarns. Design/methodology/approach – A numerical program, based on a spectral element method, is used to assess the heating fabric with a temperature control model. The study determines suitable parameters for the fabric by evaluating the temperature uniformity on the fabric surface. Effective thermal conductivities of the fabric are obtained by comparing the experimental and numerical results with each other, using a nonlinear least-square fitting method. Findings – The results indicate that employing high effective thermal conductivity of non-electric conductive yarns in a direction perpendicular to electric conductive yarns helps to increase temperature uniformity. However, the effect of the high effective thermal conductivity of electric conductive yarns is not evident. Adopting a short distance between the electric conductive yarns and a thick fabric is also beneficial in increasing temperature uniformity. If the heating fabric is applied in a place where there is easy energy transfer between the surface of the fabric and moving air, collocation with high heating power is needed to maintain the temperature. Choosing an appropriate heating source is essential when considering temperature uniformity and energy savings using a temperature controller. Originality/value – The findings will be useful in the design of heating fabrics. [ABSTRACT FROM AUTHOR]

Abstract: A three-dimensional boundary element solution for the seepage analysis in multi-domain general anisotropic media has been developed based on the transformation approach. Using analytical eigenvalues and eigenvectors of the hydraulic conductivity tensor, a closed-form coordinate transformation matrix has been provided to transform the quadratic form of governing equation of seepage for the general anisotropic media to the Laplace equation. This transformation allows the analysis to be carried out using any standard BEM codes for the potential theory on the transformed space by adding small pre- and post-processing routines. With this transformation, any physical quantity like the total head remains unchanged at corresponding nodes on the physical and transformed space, and the normal gradient across the domain boundaries should also be transformed. In multi-domain problems, compatibility equations (equality of the potential on corresponding nodes on the interface) and equilibrium equations (conservation of the flux across the interface boundaries of adjacent domains) on the corresponding nodes of interface between two neighbor domains are needed for boundary element method. In the transformed space, the compatibility equation remains unchanged. However, due to the distortion of boundaries in the mapped space and therefore misalignment of the unit outward normal vectors along the inter-domain boundaries, the equilibrium of the normal fluxes have to be transformed accordingly. Based on the proposed transformation, the normal to boundary flux boundary conditions in the mapped space and the transformed equilibrium equation for interface of adjacent zones have been given in this paper. Examples have been solved with the proposed scheme and the results were verified with the finite element method. Excellent agreement of the results shows the veracity of the proposed transformation and the formulas given for transformation of equilibrium equation for multi-domain general anisotropic media. [Copyright &y& Elsevier]

Abstract: Analytical estimates are obtained for the effective constitutive response of porous viscoplastic materials consisting of aligned ellipsoidal voids that are distributed randomly with “ellipsoidal” symmetry in the matrix material. These estimates are obtained by means of a novel iterative homogenization strategy recently proposed by Ponte Castañeda (2012), and can be shown to be bounds for certain classes of multi-scale microstructures. By design, the resulting constitutive model agrees exactly with the earlier “variational linear comparison” model at the first iteration (N=1), and provides estimates that get progressively more accurate as the number of iterations increases (), especially for high-triaxiality loading conditions, and low porosity and strain-rate sensitivity. However, in practice, a small number of iterations () is sufficient to get very accurate results. It is important to emphasize that, unlike other models that have been proposed in the literature, the new model requires no fitting parameters, solely depending on the properties of the matrix phase and microstructural information, such as the porosity, the average void shape and orientation, as well as the generally different shape and orientation of their distribution. Results are given for the yield and gauge surfaces of ideally plastic and power-law viscoplastic porous materials for the special cases of aligned spheroidal and ellipsoidal voids, and the results are compared with available numerical results and with the results of other models. Compared to available numerical results, the new estimates are found to be quite accurate, while they also provide more flexibility than competing models in terms of the characterization of the microstructure. In particular, it was found that the effect of different shapes for the average pore shape and distribution on the yield surfaces of the porous materials can be significant at high triaxialities, even for very small porosities. In addition, consistent estimates are obtained for the average strain rate in the voids, and explicit results have been computed for initially spherical voids, which exhibit a strong effect of the triaxiality, especially at low porosities and strain-rate sensitivities. [Copyright &y& Elsevier]

Abstract: Flow patterns produced by linear diffusers are highly dependent on the turbulent momentum exchange process. Hence a realistic computation of indoor room airflows that are produced from plane wall and free jets requires an accurate prediction of the anisotropic turbulent stresses. This is particularly the case in regions near the wall and entrainment effects which are caused by the turbulent shear stresses. For this reason a non-linear eddy viscosity assumption is presented which can be adjusted to account for the turbulent mixing process in the free shear flow region, and to reproduce the redistribution of the turbulent normal stresses near the wall. Based on several test cases such as a free and plane wall jet, IEA (International Energy Agency) Annex 20 room airflow, and a 3D room with a partition, the essential characteristics of the linear and non-linear k–ε, k–ω and ν 2–f turbulence models are analysed. Thereby it is shown that the proposed non-linear assumption can improve the prediction of linear diffuser airflows. [Copyright &y& Elsevier]

Abstract: A numerical computer model based on the dual reciprocity boundary element method (DRBEM) is extended to study the generalized theories of magneto-thermoelasticity problems in a rotating anisotropic viscoelastic functionally graded solid placed in a constant primary magnetic field acting in the direction of the z-axis and rotating about this axis with a constant angular velocity. In the case of plane deformation, a predictor–corrector implicit–explicit time integration algorithm was developed and implemented for use with the DRBEM to obtain the solution for the displacement and temperature fields in the context of the Green and Naghdi theory of type III. A comparison of the results is presented graphically in the absence and presence of magnetic field. Numerical results that demonstrate the validity of the proposed method are also presented graphically. [Copyright &y& Elsevier]

Abstract: This paper develops the Somigliana type boundary integral equations for fracture of anisotropic thermoelastic solids using the Stroh formalism and the theory of analytic functions. In the absence of body forces and internal heat sources, obtained integral equations contain only curvilinear integrals over the solid’s boundary and crack faces. Thus, the volume integration is eliminated and also there is no need to evaluate integrals over the contours in the mapped temperature domain as it was done before. In addition to finite solids, the case of an infinite anisotropic medium with a remote thermal load is also studied. The dual boundary element method for fracture of anisotropic thermoelastic solids is developed based on the obtained boundary integral equations. Presented numerical examples show the validity and efficiency of the obtained equations in the analysis of both finite and infinite solids with cracks. [Copyright &y& Elsevier]

Abstract: The dynamic response of plane inhomogeneous anisotropic bodies made of linear viscoelastic materials is investigated. The mechanical behavior of the viscoelastic material is described by differential constitutive equations with fractional order derivatives. The governing equations, which are derived by considering the dynamic equilibrium of the plane body element, are two coupled linear fractional evolution partial differential equations in terms of the displacements, whose order is in general greater than two with respect to time derivatives. A method is presented to establish the additional required initial conditions beside the described initial displacements and velocities. Using the Analog Equation Method (AEM) in conjunction with the Domain Boundary Element Method (D/BEM) the governing equations are transformed into a system of multi-term ordinary fractional differential equations (FDEs), which are solved using the numerical method for multi-term FDEs developed recently by Katsikadelis. Numerical examples are presented, which not only demonstrate the efficiency of the solution procedure and validate its accuracy, but also permit a better understanding of the dynamic response of plane bodies described by different viscoelastic models. [Copyright &y& Elsevier]

Abstract: Constitutive equations for elastically anisotropic nonlinear elastic–viscoplastic solids are often formulated assuming that the strain energy function depends on an elastic deformation gradient. Also, dependence on a triad of vectors can be introduced to characterize directions of material anisotropy. The elastic deformation gradient is usually written in terms of the total deformation gradient and a plastic deformation gradient, together with a specification of the reference configuration. Alternatively, it is possible to introduce a triad of microstructural vectors which are determined by integrating evolution equations and which characterize the elastic response and orientations of directions of anisotropy. The objective of this paper is to demonstrate that the elastic, total and plastic deformation measures and the vectors used to characterize directions of material anisotropy contain unphysical arbitrariness which prevents them from being measured. In contrast, the microstructural vectors used in the alternative formulation can be measured and remove this unphysical arbitrariness. [Copyright &y& Elsevier]

Abstract: The main objective of this paper is to study the transient magneto-thermo-visco-elastic stresses in a non-homogeneous anisotropic solid placed in a constant primary magnetic field acting in the direction of the z-axis and rotating about it with a constant angular velocity. The system of fundamental equations is solved by means of a dual-reciprocity boundary element method (DRBEM). In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are carried out for the temperature, displacement components and thermal stress components. The validity of DRBEM is examined by considering a magneto-thermo-visco-elastic solid occupies a rectangular region and good agreement is obtained with the results obtained by other methods. The results obtained are presented graphically to show the effect of inhomogeneity on the displacement components and thermal stress components. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze the electromechanical instability of anisotropic dielectric elastomers. When an electric field and biaxial stress are applied to a dielectric elastomer, the homogeneous deformation of the dielectric elastomer may be unstable and pull-in instability and bifurcation instability may occur. Based on the previous investigations on the incompressible anisotropic elastic solids and dielectric elastomers, we outline the theory of anisotropic dielectrics. The electromechanical instability is considered for a thin layer of a dielectric elastomer sandwiched between two compliant electrodes. Analytic solutions are obtained for the classic neo-Hookean model of anisotropic materials. The results show that the stability of the dielectric elastomer is remarkably enhanced by anisotropy parameter. [Copyright &y& Elsevier]

Abstract: This presentation is mainly devoted to the research on the regularization of indirect boundary integral equations (IBIEs) for anisotropic potential problems. Based on a new idea, a novel regularization technique is pursued, in which the regularized IBIEs excluding the CPV and HFP integrals are established. The proposed method has many advantages. First, it does not need to calculate multiple integral as the Galerkin method, so it is simple and easy for programming. Second, it can compute boundary quantities ∂u/∂x i (i=1,2). Third, the anisotropic problems can be solved directly without transforming them into isotropic ones so that no inverse transform is required. Finally, the gradient BIEs are independent of the potential BIEs and they can provide variously useful equations. Numerical examples show that a better precision and high computational efficiency can be achieved by the present method. [Copyright &y& Elsevier]

Abstract: In a recent paper Destrade studied surface waves in an exponentially graded orthotropic elastic material. He showed that the quartic equation for the Stroh eigenvalue p is, after properly modified, a quadratic equation in p 2 with real coefficients. He also showed that the displacement and the stress decay at different rates with the depth x 2 of the half-space. Vinh and Seriani considered the same problem and added the influence of gravity on surface waves. In this paper we generalize the problem to exponentially graded general anisotropic elastic materials. We prove that the coefficients of the sextic equation for p remain real and that the different decay rates for the displacement and the stress hold also for general anisotropic materials. A surface wave exists in the graded material under the influence of gravity if a surface wave can propagate in the homogeneous material without the influence of gravity in which the material parameters are taken at the surface of the graded half-space. As the wave number k →∞, the surface wave speed approaches the surface wave speed for the homogeneous material. A new matrix differential equation for surface waves in an arbitrarily graded anisotropic elastic material under the influence of gravity is presented. Finally we discuss the existence of one-component surface waves in the exponentially graded anisotropic elastic material with or without the influence of gravity. [Copyright &y& Elsevier]

Abstract: It is known that an anti-plane shear surface wave does not exist in anisotropic elastic half-space x 2 ⩾0 when the material is homogeneous. For a functionally graded material for which the elastic stiffness C 44, C 45, C 55 and the mass density ρ depend on the depth x 2 of the half-space, an anti-plane shear surface wave may exist. Exact solutions for four cases of special graded materials are presented here. In all four cases C 44 and ρ have the same function form. C 55 and C 45 are related but they need not have the same function form as C 44 and ρ. In fact C 45 can depend on x 2 arbitrarily. In Case 4, C 44 and ρ are periodic function in x 2. For a general graded material, an asymptotic solution for large wave number k is obtained and conditions for the existence of an anti-plane shear surface wave are presented. Regardless of exact or asymptotic solutions, as k →∞, the surface wave speed v approaches which is the speed of the exceptional body wave evaluated for the material property at x 2 =0. The surface wave solution has an interesting phenomenon when the elastic stiffness C 45 is non-zero. [Copyright &y& Elsevier]

Abstract: We consider an anisotropic elastic inclusion of arbitrary shape embedded inside an infinite dissimilar anisotropic elastic medium (matrix) subjected to a uniform antiplane shear loading at infinity. In contrast to the corresponding results from linear isotropic elasticity, we show that for certain anisotropic materials, despite the limitation of perfect bonding between the inclusion and its surrounding matrix, it is possible to design an arbitrarily shaped (not necessarily elliptic) inclusion so that the interior stress distribution is uniform provided the shear stress in the matrix (of dissimilar anisotropic material) is also uniform. Further, in the case when the bonding between the inclusion and the matrix is assumed to be imperfect, we show that for the stress distribution inside the inclusion to be uniform, the inclusion must be elliptical. [Copyright &y& Elsevier]

Abstract: It is known that a subsonic surface (Rayleigh) wave exists in an anisotropic elastic half-space x 2 ⩾0 if the first transonic state is not of Type 1. If the first transonic state is of Type 1 but the limiting wave is not exceptional, a subsonic surface wave exists. If the first transonic state is of Type 1 and the limiting wave is exceptional, a subsonic surface wave exists when . It is shown that an exceptional body wave is necessarily an exceptional transonic wave, and could be an exceptional limiting wave. Only two wave speeds are possible for an exceptional body wave. We present explicit conditions in terms of the reduced elastic compliances for the existence of an exceptional body wave. If an exceptional body wave exists, conditions are given for identifying whether the transonic state is of Type 1. Hence, through the existence of an exceptional body wave we provide explicit conditions for the existence of a subsonic surface wave with the exception when needs to be computed. [Copyright &y& Elsevier]

Abstract: An anisotropic finite deformation thermodynamic framework is developed that admits most of the models within the class of unified viscoplasticity approaches, applying to representations of the behaviors of polymers, metals and their composites. The importance of changing natural configurations as a driver for dissipation is emphasized, as is the specification of constitutive behaviors via the energy and dissipation functions. In a sequential application of thermodynamic approaches, Caratheodory’s lemma is first applied to establish traditional potential relations for the stress and entropy, followed by application of the Coleman–Noll approach to deduce that evolution functions related to the rates of the independent variables must be associated with reversible, non-dissipative changes. The principal of maximum dissipation is lastly applied to deduce the flow rule, identify dissipative behaviors, and deduce interrelationships between the independently-specified energy and dissipation functions. A simplified case is described that illustrates these interrelationships and their compatibilities with the proposed framework. [Copyright &y& Elsevier]

Abstract: In this paper we study the evolution of pressure of a single-phase, slightly compressible fluid in a porous medium where a non-permeable wellbore is present. The flow is induced by a single probe on the side of an otherwise sealed wellbore which is drilled at an angle to the vertical into the anisotropic rock formation. The formulation is derived by giving a transient correction due to the presence of the wellbore to the time dependent free space source field solution (the probe). Using the divergence theorem and the zero flux condition on the wellbore surface, a boundary element formulation is derived and solved numerically in the Laplace and Fourier transformed domain before being inverse-transformed to give the real time behaviour. [Copyright &y& Elsevier]

Abstract: The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress–strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress–strain behavior on the MWNT content for both uniaxial tension and uniaxial compression. [Copyright &y& Elsevier]

Abstract: This paper investigates the plane stress problem of generally anisotropic magneto-electro-elastic beams with the coefficients of elastic compliance, piezoelectricity, dielectric impermeability, piezomagnetism, magnetoelectricity, and magnetic permeability being arbitrary functions of the thickness coordinate. Firstly, partial differential equations governing stress function, electric displacement function and magnetic induction function are derived for plane problems of anisotropic functionally graded magneto-electro-elastic materials. Secondly, these functions are assumed in forms of polynomials in the longitudinal coordinate and can be acquired through a successive integral approach. The analytical expressions of axial force, bending moment, shear force, average electric displacement, average magnetic induction, displacements, electric potential and magnetic potential are then deduced. Thirdly, problems of functionally graded magneto-electro-elastic plane beams are considered, with integral constants being completely determinable from boundary conditions. A series of analytical solutions are thus obtained, including the solutions for beams under tension and pure bending, for cantilever beams subjected to shear force applied at the free end, and for cantilever beams subjected to uniform load. These solutions can be easily degenerated into the solutions for homogenous anisotropic magneto-electro-elastic beams. Finally, a numerical example is presented to show the application of the proposed method. [Copyright &y& Elsevier]

Abstract: A continuum model describing sea ice as a layer of granulated thick ice, consisting of many rigid, brittle floes, intersected by long and narrow regions of thinner ice, known as leads, is developed. We consider the evolution of mesoscale leads, formed under extension, whose lengths span many floes, so that the surrounding ice is treated as a granular plastic. The leads are sufficiently small with respect to basin scales of sea ice deformation that they may be modelled using a continuum approach. The model includes evolution equations for the orientational distribution of leads, their thickness and width expressed through second-rank tensors and terms requiring closures. The closing assumptions are constructed for the case of negligibly small lead ice thickness and the canonical deformation types of pure and simple shear, pure divergence and pure convergence. We present a new continuum-scale sea ice rheology that depends upon the isotropic, material rheology of sea ice, the orientational distribution of lead properties and the thick ice thickness. A new model of lead and thick ice interaction is presented that successfully describes a number of effects: (i) because of its brittle nature, thick ice does not thin under extension and (ii) the consideration of the thick sea ice as a granular material determines finite lead opening under pure shear, when granular dilation is unimportant. [Copyright &y& Elsevier]

Abstract: In this paper, a dual-reciprocity boundary element method based on some polynomial interpolations to the time-dependent variables is presented for the numerical solution of a two-dimensional heat conduction problem governed by a third order partial differential equation (PDE) over a homogeneous anisotropic medium. The PDE is derived using a non-Fourier heat flux model which may account for thermal waves and/or microscopic effects. In the analysis, discontinuous linear elements are used to model the boundary and the variables along the boundary. The systems of algebraic equations are set up to solve all the unknowns. For the purpose of evaluating the proposed method, some numerical examples with known exact solutions are solved. The numerical results obtained agree well with the exact solutions. [Copyright &y& Elsevier]

Abstract: In this study, the transition from transient to steady-state responses for anisotropic layered media subjected to antiplane time harmonic loading is investigated. To solve this complicated problem, a linear coordinate transformation is introduced and successfully used to transform the anisotropic layered medium problem to an isotropic problem. The transient responses are obtained by the convolution of time harmonic loading function with transient solutions derived analytically from an effective matrix method. The steady-state problem is solved by applying the wave number integral representation. For numerical calculations, the transient and steady-state responses of an anisotropic thin layer overlying a half-space are considered. The transition behavior from transient solution to steady state is presented and discussed in detail. [Copyright &y& Elsevier]

Abstract: Thermomagnetoelectroelastic problems for various defects embedded in an infinite matrix are considered in this paper. Using Stroh''s formalism, conformal mapping, and perturbation technique, Green''s functions are obtained in closed form for a defect in an infinite magnetoelectroelastic solid induced by the thermal analog of a line temperature discontinuity and a line heat source. The defect may be of an elliptic hole or a Griffith crack, a half-plane boundary, a bimaterial interface, or a rigid inclusion. These Green''s functions satisfy the relevant boundary or interface conditions. The proposed Green''s functions can be used to establish boundary element formulation and to analyzing fracture behaviour due to the defects mentioned above. [Copyright &y& Elsevier]

To noninvasively assess the risk of aneurysm rupture and dissection, an accurate material failure metric of the aortic wall is crucial. Previous studies used deterministic or isotropic failure metrics for the aortic wall. However, experimental studies have shown that aortic wall tensile strengths in circumferential and axial directions are significantly different (i.e., anisotropic) and vary greatly among patients. In this study, we developed a new probabilistic and anisotropic material failure metric for rupture risk assessment of ascending thoracic aortic aneurysm (ATAA). We performed uniaxial tensile failure tests using aortic tissue samples of 84 ATAA patients, from which a joint probability distribution of the anisotropic wall strengths was obtained. Subsequently, we derived an anisotropic failure probability (FP) metric based on the Tsai-Hill (TH) failure criterion. The novel FP metric incorporates uncertainty and anisotropy of failure properties. To compare the FP metric with traditional deterministic and isotropic metrics, we numerically estimated "baseline" risks of additional 41 ATAA patients using matching CT images and tissue testing data. We presented different risk assessment methods (e.g., with and without patient-specific hyperelastic properties) and compared them using receiver operating characteristic (ROC) curves. The results demonstrated that: (1) the probabilistic FP metric outperforms the deterministic TH metric and the isotropic maximum principal stress; (2) patient-specific hyperelastic properties can help to improve the performance of probabilistic FP metric in ATAA risk assessment. The proposed probabilistic modeling framework may be adopted for other types of materials. [ABSTRACT FROM AUTHOR]

Let { X (t) , t ∈ M } and { Z (t ′) , t ′ ∈ M ′ } be smooth Gaussian random fields parameterized on Riemannian manifolds M and M ′ , respectively, such that X (t) = Z (f (t)) , where f : M → M ′ is a diffeomorphic transformation. We study the expected number and height distribution of the critical points of X in connection with those of Z. As an important case, when X is an anisotropic Gaussian random field, then we show that its expected number of critical points becomes proportional to that of an isotropic field Z , while the height distribution remains the same as that of Z. [ABSTRACT FROM AUTHOR]