A gradient theory of finite viscoelasticity

Abstract

In this paper we present a gradient theory of finite viscoelasticity. The theory is founded on the concept of internal fields, in conjunction with a variational principle and the dissipation inequality. The internal variables, which in local theories obey local evolution equations, have been replaced by internal fields and their gradients, which arise from physical processes that involve non-affine deformation. At variance with the local theory, these fields obey "internal" field equations and appropriate boundary and initial conditions. As a result, uniform boundary tractions give rise to inhomogeneous strain fields. This phenomenon is illustrated in one dimension, where it is shown that the creep function, normally a function of time only, is a function of space as well as time, even though the material domain is phenomenologically homogeneous.