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2D boundary element analysis of defective thermoelectroelastic bimaterial with thermally imperfect but mechanically and electrically perfect interface
Abstract
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.
... Due to the brittle nature of ceramics, there is a need for additional research into the applicability limits of such FGM structures [38][39][40]. The complexity of the geometry of structural elements and consideration of imperfections in the contact of their components stimulate the process of improving mathematical models of FGMs to ensure their qualitative design both in terms of mechanical strength [12][13][14][41][42][43][44][45][46][47][48][49][50][51][52][53][54] and in terms of consideration of thermal, magnetic, piezoelectric loading factors [47,48]. The use of the FGMs seems to be one of the most effective materials in the realization of sustainable development in industries. ...
... Due to the brittle nature of ceramics, there is a need for additional research into the applicability limits of such FGM structures [38][39][40]. The complexity of the geometry of structural elements and consideration of imperfections in the contact of their components stimulate the process of improving mathematical models of FGMs to ensure their qualitative design both in terms of mechanical strength [12][13][14][41][42][43][44][45][46][47][48][49][50][51][52][53][54] and in terms of consideration of thermal, magnetic, piezoelectric loading factors [47,48]. The use of the FGMs seems to be one of the most effective materials in the realization of sustainable development in industries. ...
... The following entries [47,49] shall continue to apply: ...
Within the framework of the concept of deformable solid mechanics, an analytical numerical method to the problem of determining the mechanical fields in the composite structures with interphase ribbon-like deformable multilayered inhomogeneities under combined force and dislocation loading has been proposed. Based on the general relations of linear elasticity theory, a mathematical model of thin multilayered inclusion of finite width is constructed. The possibility of
nonperfect contact along a part of the interface between the inclusion and the matrix, and between the layers of inclusion where surface energy or sliding with dry friction occurs, is envisaged. Based on the application of the theory of functions of a complex variable and the jump function method, the stress-strain field in the vicinity of the inclusion during its interaction with the concentrated forces and screw dislocations was calculated. The values of generalized stress intensity factors for the
asymptotics of stress-strain fields in the vicinity of the ends of thin inhomogeneities are calculated, using which the stress concentration and local strength of the structure can be calculated. Several effects have been identified which can be used in designing the structure of layers and operation modes of such composites. The proposed method has shown its effectiveness for solving a whole class of problems of deformation and fracture of bodies with thin deformable inclusions of finite length
and can be used for mathematical modeling of the mechanical effects of thin FGM heterogeneities in composites.
... Due to the brittle nature of ceramics, there is a need for additional research into the applicability limits of such FGM structures [38][39][40]. The complexity of the geometry of structural elements and consideration of imperfections in the contact of their components stimulate the process of improving mathematical models of FGMs to ensure their qualitative design both in terms of mechanical strength [12][13][14][41][42][43][44][45][46][47][48][49][50][51][52][53][54] and in terms of consideration of thermal, magnetic, piezoelectric loading factors [47,48]. The use of the FGMs seems to be one of the most effective materials in the realization of sustainable development in industries. ...
... Due to the brittle nature of ceramics, there is a need for additional research into the applicability limits of such FGM structures [38][39][40]. The complexity of the geometry of structural elements and consideration of imperfections in the contact of their components stimulate the process of improving mathematical models of FGMs to ensure their qualitative design both in terms of mechanical strength [12][13][14][41][42][43][44][45][46][47][48][49][50][51][52][53][54] and in terms of consideration of thermal, magnetic, piezoelectric loading factors [47,48]. The use of the FGMs seems to be one of the most effective materials in the realization of sustainable development in industries. ...
... The following entries [47,49] shall continue to apply: ...
Within the framework of the concept of deformable solid mechanics, an analytical-numerical method to the problem of determining the mechanical fields in the composite structures with interphase ribbon-like deformable multilayered inhomogeneities under combined force and dislocation loading has been proposed. Based on the general relations of linear elasticity theory, a mathematical model of thin multilayered inclusion of finite width is constructed. The possibility of nonperfect contact along a part of the interface between the inclusion and the matrix, and between the layers of inclusion where surface energy or sliding with dry friction occurs, is envisaged. Based on the application of the theory of functions of a complex variable and the jump function method, the stress-strain field in the vicinity of the inclusion during its interaction with the concentrated forces and screw dislocations was calculated. The values of generalized stress intensity factors for the asymptotics of stress-strain fields in the vicinity of the ends of thin inhomogeneities are calculated, using which the stress concentration and local strength of the structure can be calculated. Several effects have been identified which can be used in designing the structure of layers and operation modes of such composites. The proposed method has shown its effectiveness for solving a whole class of problems of deformation and fracture of bodies with thin deformable inclusions of finite length and can be used for mathematical modeling of the mechanical effects of thin FGM heterogeneities in composites.
... In the case of 2D thermoelectroelasticity of anisotropic solids a general complex variable approach was developed based on the Stroh formalism, which results in truly boundary integral formulae and equations for inhomogeneous [7], half-space [8] and bimaterial [9,10] solids. Also it was shown that the kernels of boundary integral equations are closely related to the Green's functions of thermoelectroelasticity [7]. ...
... where ∂B is a boundary of the domain B; n p is a unit outwards normal vector to the surface ∂B. Assuming that the tensor k pq is an identity tensor (k pq ¼ δ pq , where δ pq is a Kronecker delta) Eq. (10) transforms into the Green's second integral identity ∬ ∂B ϕψ ;p À ψϕ ;p n p dS ¼ ∭ B ϕψ ;pp À ψϕ ;pp dV: ...
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.
... Successful attempts were made in [17,33,[42][43][44][45] to apply it to consider the influence of various physical and contact nonlinearities in the antiplane problem of elasticity theory for two compressed half-spaces with interfacial defects. The frictional slip with possible heat generation for contacting bodies [34,44,[46][47][48][49] and the boundary element approach [50][51][52] were also considered here. Inhomogeneity of the mechanical properties of structural materials can be both designed for a specific purpose (FGM) and a consequence of technological processes of obtaining new materials and their processing (FSW, ball-burnishing process, etc.) [53,54]. ...
The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress–strain state of a piecewise homogeneous linear–elastic matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is constructed. An analytic–numerical analysis of the stress fields for some typical cases of the continuous functional gradient dependence of the mechanical
properties of the inclusion material is performed. It is proposed to apply the constructed solutions to select the functional gradient properties of the inclusion material to optimize the stress–strain state in its vicinity under the given stresses. The derived equations are suitable with minor modifications for the description of micro-, meso- and nanoscale inclusions. Moreover, the conclusions and calculation
results are easily transferable to similar problems of thermal conductivity and thermoelasticity with possible frictional heat dissipation
... Successful attempts were made in [17,33,[42][43][44][45] to apply it to consider the influence of various physical and contact nonlinearities in the antiplane problem of elasticity theory for two compressed half-spaces with interfacial defects. The frictional slip with possible heat generation for contacting bodies [34,44,[46][47][48][49] and the boundary element approach [50][51][52] were also considered here. Inhomogeneity of the mechanical properties of structural materials can be both designed for a specific purpose (FGM) and a consequence of technological processes of obtaining new materials and their processing (FSW, ball-burnishing process, etc.) [53,54]. ...
The effect of a functional gradient in the cross-section material (FGM) of a thin ribbon-like interfacial deformable inclusion on the stress–strain state of a piecewise homogeneous linear–elastic matrix under longitudinal shear conditions is considered. Based on the equations of elasticity theory, a mathematical model of such an FGM inclusion is constructed. An analytic–numerical analysis of the stress fields for some typical cases of the continuous functional gradient dependence of the mechanical properties of the inclusion material is performed. It is proposed to apply the constructed solutions to select the functional gradient properties of the inclusion material to optimize the stress–strain state in its vicinity under the given stresses. The derived equations are suitable with minor modifications for the description of micro-, meso- and nanoscale inclusions. Moreover, the conclusions and calculation results are easily transferable to similar problems of thermal conductivity and thermoelasticity with possible frictional heat dissipation.
... It is widely used in the analysis of anisotropic [6], [7], piezoelectric [7], [15], [16] and magnetoelectroelastic [15] solids with through cracks and inclusions. In [3], [4], boundary integral Somilliana-type equations for the boundary-element analysis of anisotropic thermomagnetoelectroelastic bimaterial with holes, cracks and thin inclusions are obtained. ...
This work studies the problem of thermomagnetoelectroelastic anisotropic bimaterial with imperfect high-temperature conducting coherent interface, whose components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus, the Somigliana-type integral formulae and the corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high-temperature conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented for single and multiple inclusions.
An analytical–numerical method for solving the class of problems of determining mechanical fields in composite structures with interfacial ribbon-like deformable multilayer physically nonlinear inhomogeneities under combined force and dislocation loading is proposed. The mathematical model of thin inclusion of material with arbitrary mechanical properties is constructed. The possibility of the existence of an imperfect contact along the part of the interface between the inclusion and the matrix, as well as between the layers of the inclusion, where there is surface energy or sliding with dry friction, is provided. Based on the method of jump functions, the stress–strain field in the vicinity of the inclusion at its interaction with concentrated forces and helical dislocations is calculated. The values of the generalized stress intensity coefficients for the asymptotic of the stress–strain fields in the vicinity of the ends of thin inhomogeneities are calculated, which can be used to calculate the stress concentration and local strength of the structure. Several new effects that can be used in the design of the structure of layers and modes of operation of such composites are revealed.
An incremental approach to solving the antiplane problem for bimaterial media with a thin, physically nonlinear inclusion placed on the materials interface is discussed. Using the jump functions method and the coupling problem of boundary values of the analytical functions method we reduce the problem to the system of singular integral equations (SSIE) on jump functions with variable coefficients allowing us to describe any quasi-static loads (monotonous or not) and their influence on the stress-strain state in the bulk. To solve the SSIE problem, an iterative analytical-numerical method is offered for various non-linear deformation models. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analyzed for a deformed body under a load of a balanced concentrated force system.
Due to extensive applications in engineering practice, analysis of heat transfer in three-dimensional anisotropic composites has remained to be an important research topic. For the analysis, conventional numerical methods face modeling difficulties to different degrees when the thickness of component is very small. For this, modeling thin adhesive/interstitial media is usually ignored in conventional analyses. In this paper, two different boundary-element approaches are presented to model the heat conduction in three-dimensional anisotropic composites with thin adhesive/interstitial media. The first one is to weaken the singularity of the nearly singular boundary integrals, and the second is to implement a boundary-element conductance model without treating the thin media. All formulations have been implemented with illustrations of a few benchmark examples in the end.
This work studies the problem of a thermomagnetoelectroelastic anisotropic bimaterial with imperfect high temperature-conducting coherent interface, which components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus the Somigliana type integral formulae and corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high temperature-conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented.
This article provides a perspective on the current status of the formulations of dual boundary element methods with emphasis on the regularizations of hypersingular integrals and divergent series. A simple example is given to show the dual integral representation and the dual series representation for a discontinuous function and its derivative and thereby to illustrate the regularization problems encountered in dual boundary element methods. Hypersingularity and the theory of divergent series are put under the framework of the dual representations, their relation and regularization techniques being examined. Applications of the dual boundary element methods using hypersingularity and divergent series are explored. This review article contains 249 references.
By means of the extended version of the Stroh formalism for uncoupled thermo-anisotropic elasticity, two-dimensional Green’s
function solutions in terms of exponential integrals are derived for the thermoelastic problem of a line heat source and a
temperature dislocation near an imperfect interface between two different anisotropic half-planes with different thermo-mechanical
properties. The imperfect interface investigated here is modeled as a generalized spring layer with vanishing thickness: (1)
the normal heat flux is continuous at the interface, whereas the temperature field undergoes a discontinuity which is proportional
to the normal heat flux; (2) the tractions are continuous across the interface, whereas the displacements undergo jumps which
are proportional to the interface tractions. This kind of imperfect interface can be termed a thermally weakly conducting
and mechanically compliant interface. In the Appendix we also present the isothermal Green’s functions in anisotropic bimaterials
with an elastically stiff interface to demonstrate the basic ingredients in the analyses of a stiff interface.
The paper presents a complex variable approach for obtaining of the integral formulae and integral equations for plane thermoelectroelasticity of an anisotropic bimaterial with thermally insulated interface. Obtained relations do not contain domain integrals and incorporate only physical boundary functions such as temperature, heat flux, extended displacement and traction, which are the main advances of these relations.
On the basis of the general integral equations of thermoelectroelasticity deduced earlier for bodies with thin heterogeneities, we construct an analytic solution of the plane problem for a pyroelectric body containing a crack whose faces are kept at a constant temperature under the action of a concentrated heat source lying on the continuation of its axis. By using the principle of self-similarity, we establish the conditions under which the steady-state mode of heat conduction is attained. Compact solutions are obtained for the intensity factors of heat flows, stresses, and electric displacements. The numerical analysis of the results is performed.
Green's Function and Boundary Elements of Multifield Materials contains a comprehensive treatment of multifield materials under coupled thermal, magnetic, electric, and mechanical loads. Its easy-to-understand text clarifies some of the most advanced techniques for deriving Green's function and the related boundary element formulation of magnetoelectroelastic materials: Radon transform, potential function approach, Fourier transform. Our hope in preparing this book is to attract interested readers and researchers to a new field that continues to provide fascinating and technologically important challenges. You will benefit from the authors' thorough coverage of general principles for each topic, followed by detailed mathematical derivation and worked examples as well as tables and figures where appropriate. * In-depth explanations of the concept of Greens function * Coupled thermo-magneto-electro-elastic analysis * Detailed mathematical derivation for Greens functions.
The objective of this contribution is to develop a thermodynamically consistent theory for general imperfect coherent interfaces in view of their thermomechanical behavior and to establish a unified computational framework to model all classes of such interfaces using the finite element method. Conventionally, imperfect interfaces with respect to their thermal behavior are often restricted to being either highly conducting (HC) or lowly conducting (LC) also known as Kapitza. The interface model here is general imperfect in the sense that it allows for a jump of the temperature as well as for a jump of the normal heat flux across the interface. Clearly, in extreme cases, the current model simplifies to HC and LC interfaces. A new characteristic of the general imperfect interface is that the interface temperature is an independent degree of freedom and, in general, is not a function of only temperatures across the interface. The interface temperature, however, must be computed using a new interface material parameter, i.e., the sensitivity. It is shown that according to the second law, the interface temperature may not necessarily be the average of (or even between) the temperatures across the interface. In particular, even if the temperature jump at the interface vanishes, the interface temperature may be different from the temperatures across the interface. This finding allows for a better, and somewhat novel, understanding of HC interfaces. That is, a HC interface implies, but is not implied by, the vanishing temperature jump across the interface. The problem is formulated such that all types of interfaces are derived from a general imperfect interface model, and therefore, we establish a unified finite element framework to model all classes of interfaces for general transient problems. Full details of the novel numerical scheme are provided. Key features of the problem are then elucidated via a series of three-dimensional numerical examples. Finally, we recall since the influence of interfaces on the overall response of a body increases as the scale of the problem decreases, this contribution has certain applications to nano-composites and also thermal interface materials.
Anisotropic Elastic Plates find wide applications as structural elements in modern technology. The plates are considered to be subjected to not only inplane loads but also transverse loads. Plane problems, plate bending problems as well as stretching-bending coupling problems are all treated in this book. In addition to the introduction of the theory of anisotropic elasticity that includes two complex variable methods - Lekhnitiskii formalism and Stroh formalism- several important subjects are also discussed such as wedges, interfaces, cracks, holes, inclusions, contact problems, piezoelectric materials, thermal stresses and boundary element analysis. Anisotropic Elastic Plates also collects over one hundred problems and solutions. This book is a useful resource for engineers and researchers in composite materials. © Springer Science+Business Media, LLC 2010. All rights reserved.
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.
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.
In this paper, a new type of hybrid fundamental solution-based finite element method (HFS-FEM) is developed for analyzing plane piezoelectric problems with defects by employing fundamental solutions (or Green’s functions) as internal interpolation functions. The hybrid method is formulated based on two independent assumptions: an intra-element field covering the element domain and an inter-element frame field along the element boundary. Both general elements and a special element with a central elliptical hole or crack are developed in this work. The fundamental solutions of piezoelectricity derived from the elegant Stroh formalism are employed to approximate the intra-element displacement field of the elements, while the polynomial shape functions used in traditional FEM are utilized to interpolate the frame field. By using Stroh formalism, the computation and implementation of the method are considerably simplified in comparison with methods using Lekhnitskii’s formalism. The special-purpose hole element developed in this work can be used efficiently to model defects such as voids or cracks embedded in piezoelectric materials. Numerical examples are presented to assess the performance of the new method by comparing it with analytical or numerical results from the literature.
This paper develops Somigliana type boundary integral equations for 2D thermoelectroelasticity of anisotropic solids with cracks and thin inclusions. Two approaches for obtaining of these equations are proposed, which validate each other. Derived boundary integral equations contain domain integrals only if the body forces or distributed heat sources are present, which is advantageous comparing to the existing ones. Closed-form expressions are obtained for all kernels. A model of a thin pyroelectric inclusion is obtained, which can be also used for the analysis of solids with impermeable, permeable and semi-permeable cracks, and cracks with an imperfect thermal contact of their faces. The paper considers both finite and infinite solids. In the latter case it is proved, that in contrast with the anisotropic thermoelasticity, the uniform heat flux can produce nonzero stress and electric displacement in the unnotched pyroelectric medium due to the tertiary pyroelectric effect. Obtained boundary integral equations and inclusion models are introduced into the computational algorithm of the boundary element method. The numerical analysis of sample and new problems proved the validity of the developed approach, and allowed to obtain some new results.
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.
This paper develops integral equations and boundary element method for determination of 2D electro-elastic state of solids containing cracks, thin voids and inclusions. It proves that stress and electric displacement field near the tip of thin inhomogeneity possesses square root singularity. Thus, for determination of electromechanical fields near thin defects new special base functions are introduced. The interpolation quadratures along with the polynomial transformations are adopted for efficient numerical evaluation of singular and hypersingular integrals. Presented numerical examples show high efficiency and accuracy of the proposed approach.
In this paper, the problem of a subinterface crack in an anisotropic piezoelectric bimaterial is analyzed. A system of singular integral equations is formulated for general anisotropic piezoelectric bimaterial with kernel functions expressed in complex form. For commonly used transversely isotropic piezoelectric materials, the kernel functions are given in real forms. By considering special properties of one of the bimaterial, various real kernel functions for half-plane problems with mechanical traction-free or displacement-fixed boundary conditions combined with different electric boundary conditions are obtained. Investigations of half-plane piezoelectric solids show that, particularly for the mechanical traction-free problem, the evaluations of the mechanical stress intensity factors (electric displacement intensity factor) under mechanical loadings (electric displacement loading) for coupled mechanical and electric problems may be evaluated directly by considering the corresponding decoupled elastic (electric) problem irrespective of what electric boundary condition is applied on the boundary. However, for the piezoelectric bimaterial problem, purely elastic bimaterial analysis or purely electric bimaterial analysis is inadequate for the determination of the generalized stress intensity factors. Instead, both elastic and electric properties of the bimaterial’s constants should be simultaneously taken into account for better accuracy of the generalized stress intensity factors.
A complete set of elastic, piezoelectric, and dielectric constants is presented for the sulfides, selenides, and tellurides of zinc and cadmium. The piezoelectric constants for the hexagonal crystals in this group are markedly higher than for the cubic crystals. An elementary model theory applied to these data leads to electric charges on the metal atom increasing from +0.066 e for ZnTe to +0.84 e for CdS. The elastic compliance increases regularly with increasing anion and cation weight, with no break between the cubic and hexagonal crystals. Pyroelectric constants are given for CdS and CdSe. The quality factor of elastic resonances of CdS plates is measured as function of electric conductivity.
The thermal resistance of an interface between two materials, conceptualized by Kapitza, is an important physical phenomenon encountered in many situations of practical interest. The numerical treatment of this phenomenon has up to now run into difficulties due to the temperature discontinuity. In this work, a general and efficient computational procedure for modelling the Kapitza thermal resistance is proposed, which is based on the extended finite element method (XFEM) in tandem with a level-set method. The steady thermal conduction in a two-phase material with the Kapitza thermal resistance at the interface is first formulated in a variational way and then numerically treated with the proposed computational procedure. Different three-dimensional numerical examples with known analytical solutions show the high accuracy and robustness of the proposed computational procedure in capturing the temperature jump across an interface.
This paper presents a boundary element formulation for the analysis of linear elastic fracture mechanics problems involving anisotropic bimaterials. The most important feature associated with the present formulation is that it is a single domain method, and yet it is accurate, efficient and versatile. In this formulation, the displacement integral equation is collocated on the uncracked boundary only, and the traction integral equation is collocated on one side of the crack surface only. The complete Green's functions for anisotropic bimaterials are also derived and implemented into the boundary integral formulation so that discretization along the interface can be avoided except for the interfacial crack part. A special crack-tip element is introduced to capture exactly the crack-tip behavior.Numerical examples are presented for the calculations of stress intensity factors for a straight crack with various locations in infinite bimaterials. It is found that very accurate results can be obtained by the proposed method even with relatively coarse discretization. Numerical results also show that material anisotropy can greatly affect the stress intensity factor.
A parallel crack near the interface of magnetoelectroelastic bimaterials is considered. The crack is modelled by using the continuously distributed edge dislocations, which are described by the density functions defined on the crack line. With the aid of the fundamental solution for the edge dislocation, the present problem is reduced to a system of singular integral equations, which can be numerically solved by using the Chebyshev numerical integration technique. Then, the stress intensity factor (SIF), the magnetic induction intensity factor (MIIF) and the electric displacement intensity fac-tor (EDIF) at the crack tips are evaluated. Using these fracture criteria, the cracking behaviour of magnetoelectroelastic bimaterials is investigated. Numerical examples demonstrate that the interface, mechanical load, magnetic load and material mismatch condition are all important factors affecting the fracture toughness of the magnetoelectroelastic bimaterials.
The effective thermal‐expansion and pyroelectric coefficients of two‐phase coupled electroelastic composite materials are obtained by coupling various micromechanics theories with exact relations connecting their effective thermal and electroelastic moduli. Results are obtained for composites reinforced by ellipsoidal piezoelectric inhomogeneities and thus are applicable to a wide range of microstructural geometry including lamina, spherical particle, and continuous fiber reinforcement. The analytical framework is developed in a matrix formulation in which the electroelastic moduli are conveniently represented by a 9×9 matrix and the thermal‐expansion and pyroelectric coefficients by a 9×1 column vector. Numerical results are presented for some typical composite microstructures which show the interesting behavior of these materials.
The formulation for thermal stress and electric displacement in an infinite thermopiezoelectric plate with an interface and multiple cracks is presented. Using Green's function approach and the principle of superposition, a system of singular integral equations for the unknown temperature discontinuity defined on each crack face is developed and solved numerically. The formulation can then be used to calculate some fracture parameters such as the stresselectric displacement and strain energy density factor. The direction of crack growth for many cracks in thermopiezoelectric bimaterials is predicted by way of the strain energy density theory. Numerical results for stresselectric displacement factors and crack growth direction at a particular crack tip in two crack system of bimaterials are presented to illustrate the application of the proposed formulation.
Action of concentrated heat sources in a thermoelectroelastic medium with cracks, which faces are maintained at a constant temperature
- Pasternak