A thermodynamically consistent formulation of generalized thermoelasticity at finite deformations

TL;DR

This paper develops a thermodynamically consistent model for generalized thermoelasticity at finite deformations, capturing thermal wave propagation and ensuring stability through a Lyapunov function.

Contribution

It introduces a novel coupled non-linear thermoelastic model with additive energetic and dissipative heat flux components, ensuring thermodynamic consistency and stability.

Findings

Model accounts for thermal wave propagation.

System proven to be non-linearly stable.

Linearized model similar to Green and Naghdi type III.

Abstract

A thermodynamically consistent model of non-classical coupled non-linear thermoelasticity capable of accounting for thermal wave propagation is proposed. The heat flux is assumed to consist of both additive energetic and dissipative components. Constitutive relations for the stress, the entropy and the energetic component of the heat flux are derived in a thermodynamically consistent manner. A Lyapunov function for the dynamics is obtained for the case in which the surface of the continuum body is maintained at a reference temperature. It is shown that the system is non-linearly stable. The linearized model is shown to be similar to the type III model of Green and Naghdi, except for some minor differences in the interpretations of some of the parameters.