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

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.

arXiv commentWe have added a new section where we discuss the relation between the proposed approach and some standard concepts in the plasticity theory

References in corpus (2)

• Methodical Fitting for Mathematical Models of Rubber-like Materials
• On thermodynamics of viscoelastic rate type fluids with temperature dependent material coefficients

Cited by in corpus (5)

• A thermodynamic framework for non-isothermal phenomenological models of isotropic Mullins effect
• Implicit type constitutive relations for elastic solids and their use in the development of mathematical models for viscoelastic fluids
• The conclusion that metamaterials could have negative mass is a consequence of improper constitutive characterisation
• On the stability and convergence of Discontinuous Galerkin schemes for incompressible flow
• Numerical approximation of a thermodynamically complete rate-type model for the elastic--perfectly plastic response