ICMC 2018: Mathematics and Computing pp 309-324

# On Linear Theory of Thermoelasticity for an Anisotropic Medium Under a Recent Exact Heat Conduction Model

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 834)

## Abstract

The aim of this paper is to discuss about a new thermoelasticity theory for a homogeneous and anisotropic medium in the context of a recent heat conduction model proposed by Quintanilla (2011). The coupled thermoelasticity being the branch of science that deals with the mutual interactions between temperature and strain in an elastic medium had become the interest of researchers since 1956. Quintanilla (2011) have introduced a new model of heat conduction in order to reformulate the heat conduction law with three phase-lags and established mathematical consistency in this new model as compared to the three phase-lag model. This model has also been extended to thermoelasticity theory. Various Taylor’s expansion of this model has gained the interest of many researchers in recent times. Hence, we considered the model’s backward time expansion of Taylor’s series upto second-order and establish some important theorems. Firstly, uniqueness theorem of a mixed type boundary and initial value problem is proved using specific internal energy function. Later, we give the alternative formulation of the problem using convolution which incorporates the initial conditions into the field equations. Using this formulation, the convolution type variational theorem is proved. Further, we establish a reciprocal relation for the model.

## Keywords

Non-Fourier heat conduction model Generalized thermoelasticiy Uniqueness Variational principle Reciprocity theorem

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