Covariant spacetime formalism for applications to thermo-hyperelasticity.

The principle of material objectivity used in classical continuum mechanics states that the description of material behaviors has to be frame-invariant. Moreover, geometric considerations show that objectivity can be extended by use of a covariant principle. Covariance can be naturally expressed using a four-dimensional spacetime. We thus propose to consider a thermodynamic approach within this framework to obtain covariant constitutive models in the case of finite deformation. A four-dimensional form of the Clausius–Duhem inequality is thus derived for continuum thermomechanics applications. In this article, we are able to propose a new thermo-hyperelastic constitutive model from such a generalized thermodynamics approach with the implementation of the spacetime Lie derivative. The resulting model is then illustrated for different mechanical or thermal loadings with numerical simulations. [ABSTRACT FROM AUTHOR]