Implicit constitutive relations for describing the response of visco-elastic bodies

Abstract

A constitutive relation is proposed for viscoelastic bodies that is a generalization of the classic Kelvin–Voigt model, wherein the left Cauchy–Green tensor, the symmetric part of the velocity gradient, and the Cauchy stress tensor are implicitly related. The model developed includes several models that are being used in the literature to describe the elastic and viscoelastic response of bodies. In this paper, we study special homogeneous deformations of a slab within the context of the implicit viscoelastic model.