A thermodynamic basis for implicit rate-type constitutive relations describing the inelastic response of solids undergoing finite deformation

TL;DR

This paper develops a thermodynamic foundation for implicit rate-type constitutive relations, enhancing the theoretical understanding of inelastic responses in solids undergoing finite deformation.

Contribution

It introduces a thermodynamic basis for implicit rate-type constitutive relations, extending their application beyond purely mechanical models to include thermodynamic consistency.

Findings

Provides a thermodynamic framework for rate-type relations

Extends classical elastic-plastic models with thermodynamic consistency

Flexible framework applicable to various inelastic responses

Abstract

Implicit rate-type constitutive relations utilizing discontinuous functions provide a novel approach to the purely phenomenological description of the inelastic response of solids undergoing finite deformation. However, this type of constitutive relations has been so far considered only in the purely mechanical setting, and the complete thermodynamic basis is largely missing. We address this issue, and we develop a thermodynamic basis for such constitutive relations. In particular, we focus on the thermodynamic basis for the classical elastic--perfectly plastic response, but the framework is flexible enough to describe another types of inelastic response as well.