This article is concerned with thermoelastic behavior of an elastic media with temperature-dependent properties. The formulations of anisotropic media with variable material properties are proposed by the Clausius inequality and generalized theory of thermoelasticity with one relaxation time, where the higher-order expansion of the Helmholtz free energy with respect to increment temperature is used to obtain the relations between each parameter and real temperature. The governing equations of isotropic media with temperature-dependent properties are obtained based on these formulations. The problem of a half-space formed of an isotropic media with variable material properties and subjected to a sudden temperature rise in the boundary has been conducted. The propagations of thermoelastic wave and thermal wave, as well as the distributions of displacement, temperature, and stresses in the different cases, including constant properties and variable properties with specific temperature and real temper...

Thermoelastic behavior of elastic media with temperature-dependent properties under transient thermal shock

Asymptotic analysis of thermoelastic response in functionally graded thin plate subjected to a transient thermal shock

The prediction of thermoelastic behavior induced by transient thermal shock is important to evaluate the durability of functionally graded materials. The purpose of this article is to study the axi...

Thermoelastic interaction in functionally graded thick hollow cylinder with temperature-dependent properties

In this paper, a unified generalized thermoelastic solution with variable thermal material properties is proposed in the context of different generalized models of thermoelasticity, including thermoelasticity with one thermal relaxation time (LS theory), thermoelasticity with two thermal relaxation times (GL theory) and thermoelasticity without energy dissipation (GN theory). The unified form of governing equations is presented by introducing unifier parameters. The unified formulations are derived and given for isotropic homogenous materials with variable thermal material properties. The Laplace transform techniques and the Kirchhoff’s transformation are used to obtain general solutions for any set of boundary conditions in the physical domain. Asymptotic solutions for a specific problem of an elastic half-space with variable thermal conductivity and a specific heat, whose boundary is subjected to a thermal shock, are derived by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, some generalized thermoelastic phenomena are observed. Especially, the jumps at the wavefronts induced by the propagation of finite signal speed for the heat are clearly noticed. In addition, the effect of variable characteristics of material properties on thermoelastic behaviors is revealed by a comparison with the results obtained in the case of constant material properties.

Asymptotic solutions for generalized thermoelasticity with variable thermal material properties

Effect of fractional order parameter on thermoelastic behaviors of elastic medium with variable properties

In this paper, a new formulation for the generalized thermoelasticity in an isotropic elastic medium with temperature-dependent material properties is established. The governing equations for the generalized axisymmetric plane strain problem are derived. The asymptotic solutions for an infinite cylinder with the boundary subjected to the thermal shock are obtained under the linear assumption. Numerical results for the propagation of the thermal and elastic waves and the distributions of the displacement, temperature and stresses are given and illustrated graphically. Using these solutions, some phenomenon involved in the generalized thermoelastic problem are obtained, and the jumps at the wavefronts are observed clearly. The comparison is made with results obtained in the temperature-independent case and the influence of the temperature dependency of material properties on the propagation of thermal and elastic waves are also discussed.

Asymptotic analysis of generalized thermoelasticity for axisymmetric plane strain problem with temperature-dependent material properties

Thermal disturbance propagates in the elastic medium with a finite speed during the transient heat transfer, which leads to the thermal-mechanical behavior of materials being significantly different than that of conventional heat transfer. The axisymmetric plane strain problem is investigated in this paper, the generalized thermoelastic solutions for different generalized thermoelasticity are derived by means of the Laplace transform and its limit theorem and the asymptotic formulas of Bessel functions. A case of an infinite axisymmetric medium with a cylindrical hole under thermal shock is analyzed. It is pointed out that each of physical field has a phased distribution when the propagation of thermal disturbance with a finite speed, and both the temperature and stresses have jumps at the location of thermal elastic wavefront and thermal wavefront. The L-S and G-N theories predict similar patterns for the distributions of displacement, temperature and stresses in the transient thermal shock problem, but for G-L theory a Dirac-delta-type result for the stresses is predicted and the displacement is discontinuous at both the wavefronts.

Yingze Wang

Papers

Asymptotic analysis of generalized thermoelasticity for axisymmetric plane strain problem with temperature-dependent material properties

Generalized thermoelastic solutions for the axisymmetric plane strain problem