Problem of Statics of the Linear Thermoelasticity of the Microstretch Materials with Microtemperatures for a Half-space

We consider the statics case of the theory of linear thermoelasticity with microtemperatures and microstrech materials. The representation formula of differential equations obtained in the paper is expressed by the means of four harmonic and four metaharmonic functions. These formulas are very convenient and useful in many particular problems for domains with concrete geometry. Here we demonstrate an application of these formulas to the III type boundary value problem for a half-space. Uniqueness theorems are proved. Solutions are obtained in quadratures. 2010 Mathematics Subject Classification. 74A15, 74B10, 74F20.

On Thermoelasticity in FGL – Tolerance Averaging Technique

In this paper the problem of linear thermoelasticity in a laminate with functional gradation of properties is considered. In micro level this laminate is made of two different materials, microlaminas, distributed non-periodically but also not randomly along one of directions, what in macro level results in aforementioned functionally gradation of laminate properties. In order to describe behavior of such structure, equations of two models are here presented – the tolerance and the tolerance-asymptotic model. Both are obtained by the tolerance averaging technique. The basic aim of this work is to analyse the influence of some terms from these averaged equations on the distribution and the values of the displacements and the temperature functions. To solve the equations of two proposed models the finite difference method is used.

Linear thermoelasticity

This chapter presents a theory for the coupled thermal and mechanical response of solids under circumstances in which the deformations are small and elastic, and the temperature changes from a reference temperature are small --- a framework known as the theory of linear thermoelasticity. The basic equations of the fully-coupled linear theory of anisotropic thermoelasticity are derived. These equations are then specialized for the case of isotropic materials. Finally, as a further specialization a weakly-coupled theory in which the temperature affects the mechanical response, but the deformation does not affect the thermal response, are discussed; this is a specialization which is of importance for many engineering applications, a few of which are illustrated in the examples.

On Porous Matrices with Three Delay Times: A Study in Linear Thermoelasticity

Through the present work, we want to lay the foundation of the well-posedness question for a linear model of thermoelasticity here proposed, in which the presence of voids into the elastic matrix is taken into account following the Cowin–Nunziato theory, and whose thermal response obeys a three-phase lag time-differential heat transfer law. By virtue of the linearity of the model investigated, the basic initial-boundary value problem is conveniently modified into an auxiliary one; attention is paid to the uniqueness question, which is addressed through two alternative paths, i.e., the Lagrange identity and the logarithmic convexity methods, as well as to the continuous dependence issue. The results are achieved under very weak assumptions involving constitutive coefficients and delay times, at most coincident with those able to guarantee the thermodynamic consistency of the model.

Some basic theorems on a recent model of linear thermoelasticity for a homogeneous and isotropic medium

This paper investigates a thermoelasticity theory based on the recent heat conduction model proposed by Quintanilla ( Mech Res Commun 2011; 38: 355–360). Taylor’s expansion of this model leads to an interesting problem of heat conduction. Serious attention has been paid by researchers in the last few years to investigating various heat conduction models. We have considered this newly proposed model of heat conduction given by Quintanilla and employed for coupled thermoelastic problems. We derive the basic governing equations for a homogeneous and isotropic medium and aim to derive some important theorems. Firstly, the uniqueness theorem of a mixed initial and boundary value problem of linear thermoelasticity in the present context is proved. A variational principle is derived for the basic governing equations of motion on the basis of a functional in the context of the present problem. A reciprocity theorem is established by using Laplace transformation. Furthermore, generalization of Somigliano and Green’s theorem for this model is proved on the basis of our reciprocity relation.