Finite strain thermoelasticity and the Third Law of thermodynamics

This paper shows that commonly used large strain thermoelastic models in which the specific heat coefficient is constant or, at most, changes with temperature, are incompatible with the Third Law of thermodynamics, namely, that “entropy should be zero at the Kelvin state, that is, absolute zero temperature”. In particular, it will be shown that the Third Law implies that the specific heat coefficient must vary with deformation for the coupling between mechanical and thermal effects to take place. In line with this result, a simple analytical constitutive model consistent with the Third Law will be proposed. The model will be based on a multiplicative decomposition of the specific heat into a deformation dependent part and a temperature dependent component. The resulting thermoelastic model complies with the Third Law and, in addition, the necessary convexity conditions that ensure the existence of real wave speeds. It can replicate existing entropic elasticity models for rubber, describe melting and softening behaviour, and converge to the classical relationships for linear thermoelasticity in the small strain regime.