Implicit constitutive relations for visco-elastic solids: Part II. Non-homogeneous deformations

Abstract

A constitutive relation was developed in Part I for describing the response of a class of visco-elastic bodies, wherein the left Cauchy–Green tensor, the symmetric part of the velocity gradient, and the Cauchy stress tensor are related through an implicit constitutive relation. Here, we study a boundary value problem within the context of the model namely the inhomogeneous deformation of the body, corresponding to the response of an infinitely long slab due to the influence of gravity.