Isotropic Thermoelastic Material Research Articles

Some qualitative results in hyperbolic two-temperature generalized thermoelasticity

This study aims to establish the convolutional-type variational and reciprocity theorems within the framework of the hyperbolic two-temperature generalized thermoelasticity theory for an isotropic thermoelastic material, with the help of alternate formulation of the mixed boundary initial value problem, in which initial conditions are combined with field equations (using the Laplace transform). The convolutional-type variational principle adapts readily to numerical solutions based on the Ritz method and is useful in the finite element method. The reciprocity theorem is helpful in the theoretical development of boundary and finite element methods. The current effort can be valuable for the problem of coupling effects of thermal and mechanical fields, especially in geophysics and mining.

A mathematical model of shear wave propagation in the incompressible transversely isotropic thermoelastic half-spaces

This article deals with the problem of reflection and transmission of shear waves at a plane interface between two dissimilar incompressible transversely isotropic thermoelastic half-spaces. Two coupled quasi-shear waves are found to propagate due to the incompressibility of such materials. Applying appropriate boundary conditions at the plane interface, amplitude ratios of the reflected and transmitted quasi-shear waves are obtained. It has been observed that these ratios are functions of the angle of incidence, elastic and thermal parameters of the materials. These ratios are computed numerically for a particular model to see the effects of specific heat and thermal expansion on quasi-shear waves in incompressible transversely isotropic thermoelastic materials. The results are also presented graphically.

Fundamental solutions in the theory of thermoelastic diffusive materials with microtemperatures and microconcentrations

The main aim of this paper is to construct the fundamental solutions of a system of equations for isotropic thermoelastic diffusive materials with microtemperatures and microconcentrations in the case of steady oscillations in terms of elementary functions. In addition to this, the fundamental solutions of the system of equations of equilibrium theory of isotropic thermoelastic diffusivity materials with microtemperatures and microconcentrations are also established.

Semi-Analytical Method for Computing Effective Thermoelastic Properties in Fiber-Reinforced Composite Materials

Effective elastic and thermal properties for isotropic or transversely isotropic thermoelastic fibrous composite materials are obtained. Fibers are distributed with the same periodicity along the two perpendicular directions to the fiber orientation. The periodic cell of the composite has a square or hexagonal distribution. Perfect contact between the fiber and the matrix is presented. The effective properties are calculated using a semi-analytical method. The semi-analytical method consists of obtaining the differential equations that describe the local problems using the Asymptotic Homogenization Method. Then, these equations are solved using the Finite Element Method. Effective elastic coefficient (C¯), effective thermal expansion coefficient (α¯) and the effective thermal conductivity (κ¯) are obtained. The numerical results are compared with the semi-analytical solution and with results reported by other authors. Additionally, the effective properties for a fiber with an elliptical cross section are calculated. Distributions of the fiber’s cross section with different orientations are also studied. A MATLAB program for computing the effective coefficients is presented.

2D Quasi-Static Accurate Solutions for Isotropic Thermoelastic Materials with Applications

Thermally induced stress is an important scientific problem in engineering applications. In this paper, an accurate and efficient method for the two-dimensional quasi-static thermal elastic problem is established to explore the thermal stress problem. First, the compact quasi-static two-dimensional general solution is derived in terms of simple potential functions. The general solution is simple in form and can be derived for arbitrary boundary problems subjected to a line heat load. This is completely new to the literature. Second, Green’s function solutions of an infinite plane under the line pulse heat source based on the general solutions are presented to analyze the thermal stress field. Lastly, numerical results are taken into account to study the temperature and stress field induced by the dynamic heat source load. The corresponding analysis can constitute to reveal the mechanism of thermal elastic problems and provide some guidance for experiments or engineering structural design in the future work.

Interface Models in Coupled Thermoelasticity

This work proposes new interface conditions between the layers of a three-dimensional composite structure in the framework of coupled thermoelasticity. More precisely, the mechanical behavior of two linear isotropic thermoelastic solids, bonded together by a thin layer, constituted of a linear isotropic thermoelastic material, is studied by means of an asymptotic analysis. After defining a small parameter ε, which tends to zero, associated with the thickness and constitutive coefficients of the intermediate layer, two different limit models and their associated limit problems, the so-called soft and hard thermoelastic interface models, are characterized. The asymptotic expansion method is reviewed by taking into account the effect of higher-order terms and defining a generalized thermoelastic interface law which comprises the above aforementioned models, as presented previously. A numerical example is presented to show the efficiency of the proposed methodology, based on a finite element approach developed previously.

A General Study of Fundamental Solutions in Aniotropicthermoelastic Media with Mass Diffusion and Voids

The present paper deals with the study of a fundamental solution in transversely isotropic thermoelastic media with mass diffusion and voids. For this purpose, a two-dimensional general solution in transversely isotropic thermoelastic media with mass diffusion and voids is derived first. On the basis of the obtained general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material with mass diffusion and voids is derived by nine newly introduced harmonic functions. The components of displacement, stress, temperature distribution, mass concentration and voids are expressed in terms of elementary functions and are convenient to use. From the present investigation, some special cases of interest are also deduced and compared with the previous results obtained, which prove the correctness of the present result.

Electromagnetic, thermal and diffusive wave analysis on a two-temperature generalized thermo-elastic problem in a semi-infinite solid with cylindrical cavity subject to thermal loads

Our present work is concerned with the study of a semi-infinitely long, conducting solid with a cavity in cylindrical form in the context of magneto-thermo-elastic diffusion with two-temperature and three-phase-lag effect. The medium we have considered here is supposed to be initially quiescent. The material is assumed to be made of an isotropic homogeneous thermo-elastic material and put in a magnetic field which is uniform and acted in the direction of the axis of the cylindrical cavity. The solution to the problem is done in Laplace transform domain. Inversion process is applied to obtain the solution in space time domain and finally illustrated graphically.

Plane waves in nonlocal micropolar thermoelastic material with voids

Constitutive relations and field equations are developed for an isotropic linear micropolar thermoelastic material with voids within the context of Eringen’s theory of nonlocal elasticity. It is found that six plane waves may propagate in this medium consisting of four sets of coupled dilatational waves and two sets of coupled transverse waves. All the waves are found to be affected by the nonlocality of the medium, however, the sets of coupled transverse waves do not depend on the presence of thermal and void parameters in the medium. The dispersion relation yielding the speeds of coupled dilatational waves is analyzed, in particular, and several earlier known results are recovered from the present formulation. Numerical computations for a specific material are performed to clarify the effects of wave characteristics in detail. The computational results are displayed through graphs and explained.

Three-dimensional Green's functions for fluid and isotropic thermoelastic solid two-phase materials under heat loading

Thermal exchange between liquid and solid is a common problem for various engineering structures. The thermal stresses caused by temperature change have great influence on the engineering structures. A three dimensional model for a coupling thermal and mechanical field was established to investigate thermal stress under heat loading. In this study, the three dimensional Green's functions for fluid and isotropic thermoelastic two-phase materials with internal heat source are obtained and used to study the thermal stress problems between solid and liquid. By virtue of the compact three-dimensional general solutions expressed in harmonic functions, four newly introduced harmonic functions are constructed, and all components of coupled field are expressed in terms of elementary functions which are very convenient to use. Numerical results are given graphically by contours. The corresponding analysis will contribute to obtain stress characteristics of the fluid-solid thermal coupling field.

Effect of initial stresses on the elastic waves in transversely isotropic thermoelastic materials

In the present article, we have studied the reflection/transmission of elastic waves in initially stressed transversely isotropic thermoelastic materials. Three quasi type coupled longitudinal (QL), transverse (QT), and thermal waves are found to propagate in initially stressed transversely isotropic thermoelastic materials. For incident QL and QT‐waves at a plane interface, boundary conditions were implemented for obtaining the coefficients of reflection/transmission, the distribution of energy in the reflected and transmitted waves are also discussed. We have observed that the results vary with direction of incidence as well as the parameters due to elasticity, thermal, and initial stresses. Numerical computations have been performed and analyzed the impact of initial stresses on the results. It has been observed critical angles at θ0=30° and 58° for the reflected and transmitted QL‐waves for incident QT‐wave.

Analysis solution method for 3D planar crack problems of two-dimensional hexagonal quasicrystals with thermal effects

• An analysis solution method is proposed to analyze 3D planar crack problems for 2D hexagonal quasicrystals. • Corresponding EDD boundary integral equations are transferred to simplified integral-differential forms. • Various kinds of loadings, including normal, tangential and thermal loadings, applied on the crack are considered. • Using the proposed solution, influences of phonon-phason coupling effect on fracture parameters are assessed. An analysis solution method (ASM) is proposed for analyzing arbitrarily shaped planar cracks in two-dimensional (2D) hexagonal quasicrystal (QC) media. The extended displacement discontinuity (EDD) boundary integral equations governing three-dimensional (3D) crack problems are transferred to simplified integral-differential forms by introducing some complex quantities. The proposed ASM is based on the analogy between these EDD boundary equations for 3D planar cracks problems of 2D hexagonal QCs and those in isotropic thermoelastic materials. Mixed model crack problems under combined normal, tangential and thermal loadings are considered in 2D hexagonal QC media. By virtue of ASM, the solutions to 3D planar crack problems under various types of loadings for 2D hexagonal QCs are formulated through comparison to the corresponding solutions of isotropic thermoelastic materials which have been studied intensively and extensively. As an application, analytical solutions of a penny-shaped crack subjected uniform distributed combined loadings are obtained. Especially, the analytical solutions to a penny-shaped crack subjected to the anti-symmetric uniform thermal loading are first derived for 2D hexagonal QCs. Numerical solutions obtained by EDD boundary element method provide a way to verify the validity of the presented formulation. The influences of phonon-phason coupling effect on fracture parameters of 2D hexagonal QCs are assessed.

Enlarging quality factor in microbeam resonators by topology optimization

The fundamental characteristic of mechanical resonators can be evaluated by resonance eigenfrequency and energy dissipation (or inverse quality factor). Reduced length scales are necessary for achieving high resonance eigenfrequency, which can afford fast response and extraordinary sensitivity to external forces. However, smaller scales will result in higher energy dissipation (or smaller quality factor) in the eigenfrequency of mechanical resonators. A topology optimization process is presented for enlarging quality factor of a microbeam resonator made of linear, isotropic and homogeneous thermoelastic material. The beam’s width is supposed to be considerable so that the plane strain assumption can be satisfied and the design domain is the cross section along the beam’s thickness. By combining the equation of motion and the heat transfer equation, the damping problem of thermoelastic coupling can be solved by a finite-element method. A topology optimization method is used to enlarge quality factor in microbeam resonators. It is found by clamped-clamped and clamped-free microbeam resonators that significant improvements of quality factors can be achieved through this optimization process.

Green’s function for a line heat source acting on the surface of a coated isotropic thermoelastic material

Two-dimensional Green’s function, for a line heat source acting on the surface of a coated isotropic thermoelastic material, is investigated in this paper to improve the understanding of interface mechanisms of coating/substrate system. The coating and substrate are modeled as infinite layer and semi-infinite substrate respectively. They are perfectly bonded or are in smooth contact at the interface. Based on the two-dimensional general solution of isotropic thermoelastic materials expressed by harmonic functions, the corresponding harmonic functions with undetermined constants for coating and semi-infinite substrate are constructed, respectively. The thermoelastic field can be obtained by substituting the harmonic function into the general solution. The constants can be determined by the free surface boundary conditions and interface continuous conditions between the coating and the semi-infinite substrate. Numerical results are exhibited in the form of contours and some valuable conclusions for interface effect, interface shear debonding and coating tensile failure are presented.

Three-dimensional generalized thermoelastic diffusion and application for a thermoelastic half-space subjected to rectangular thermal pulse

ABSTRACTIn this article, a model of three-dimensional generalized thermo-diffusion in a half-space thermoelastic medium subjected to permeating gas and the rectangular thermal pulse has been constructed. The half-space is considered to be made of an isotropic homogeneous thermoelastic material. The chemical potential is also assumed to be known on the bounding plane. Laplace transform techniques have been applied, and the solution is obtained in the Laplace transform domain using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method based on a Riemann-sum approximation for the inversion of Laplace transform. The temperature increment, stress, strain, diffusion concentration, and chemical potential distributions are represented graphically. The nonzero value of the relaxation time parameter predicts the finite speed of thermal, mechanical, diffusion waves.

Extended displacement discontinuity boundary integral equation and boundary element method for cracks in thermo-magneto-electro-elastic media

The extended displacement discontinuity boundary integral equation (EDDBIE) and boundary element method is developed for the analysis of planar cracks of arbitrary shape in the isotropic plane of three-dimensional (3D) transversely isotropic thermo-magneto-electro-elastic (TMEE) media. The extended displacement discontinuities (EDDs) include conventional displacement discontinuity, electric potential discontinuity, magnetic potential discontinuity, as well as temperature discontinuity across crack faces; correspondingly, the extended stresses represent conventional stress, electric displacement, magnetic induction and heat flux. Employing a Hankel transformation, the fundamental solutions for unit point EDDs in 3D transversely isotropic TMEE media are derived. The EDDBIEs for a planar crack of arbitrary shape in the isotropic plane of a 3D transversely isotropic TMEE medium are then established. Using the boundary integral equation method, the singularities of near-crack border fields are obtained and the extended stress field intensity factors are expressed in terms of the EDDs on crack faces. According to the analogy between the EDDBIEs for an isotropic thermoelastic material and TMEE medium, an analogical solution method for crack problems of a TMEE medium is proposed for coupled multi-field loadings. Employing constant triangular elements, the EDDBIEs are discretized and numerically solved. As an application, the problems of an elliptical crack subjected to combined mechanical-electric-magnetic-thermal loadings are investigated.

Regularized MFS solution of inverse boundary value problems in three-dimensional steady-state linear thermoelasticity

We investigate the numerical reconstruction of the missing thermal and mechanical boundary conditions on an inaccessible part of the boundary in the case of three-dimensional linear isotropic thermoelastic materials from the knowledge of over-prescribed noisy data on the remaining accessible boundary. We employ the method of fundamental solutions (MFS) and several singular value decomposition (SVD)-based regularization methods, e.g. the Tikhonov regularization method (Tikhonov and Arsenin, 1986), the damped SVD and the truncated SVD (Hansen, 1998), whilst the regularization parameter is selected according to the discrepancy principle (Morozov, 1966),generalized cross-validation criterion (Golub et al., 1979) and Hansen’s L-curve method (Hansen and O’Leary, 1993).

Plane strain and three-dimensional analyses for thermo-mechanical behavior of multilayered transversely isotropic materials

An extended precise integration model for analysis of thermo-mechanical behavior of multilayered transversely isotropic materials in Cartesian coordinate system is established in this paper. From the governing equations of plane strain and three-dimensional transversely isotropic thermo-elastic materials, ordinary differential equations are derived by employing Laplace–Fourier transform. An extended precise integration model is built and solved in the transformed domain by extending the precise integration method (PIM) to multilayered thermo-elastic material system, and the actual solutions are obtained by adopting numerical quadrature schemes for the Laplace–Fourier transform inversion. The accuracy and feasibility of the proposed model is demonstrated by selected numerical examples, and then the influences of heat source’s shapes, layering, mechanical and thermal parameters of the transversely isotropic material on thermo-mechanical response are investigated.

Response of thermal source in transversely isotropic thermoelastic materials without energy dissipation and with two temperatures

A two-dimensional problem in a transversely isotropic thermoelastic medium without energy dissipation and with two temperatures due to a thermal source is investigated. As an application of the problem, a particular type of continuous thermal source has been taken to illustrate the utility of the approach. The problem is solved numerically by using a finite element method. The displacement components, conductive temperature, and stress components have been obtained numerically and illustrated graphically for our particular model. Some special cases of interest are also discussed. The implementation of finite element method codes used C++. Numerical work is also performed for a suitable material with the aim of illustrating the results.

Effect of Initial Stress on the Propagation Characteristics of Waves in Fiber-Reinforced Transversely Isotropic Thermoelastic Material under an Inviscid Liquid Layer

The present investigation deals with the propagation of waves in fiber-reinforced transversely isotropic thermoelastic solid half space with initial stresses under a layer of inviscid liquid. The secular equation for surface equation in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficients of plane waves are studied numerically for a particular model. Effects of initial stress and thickness of the layer on the phase velocity, attenuation coefficient, and specific loss of energy are predicted graphically in the certain model. A particular case of Rayleigh wave has been discussed and the dispersion curves of the phase velocity and attenuation coefficients have also been presented graphically. Some other particular cases are also deduced from the present investigation.