Modeling a class of geological materials

Abstract

In this paper we consider the development of rate type viscoelastic models from two different perspectives, using the Helmholtz potential based on the deformation gradient and the rate of entropy production, and the Gibbs potential based on the stress and the rate of entropy production. These two methods are not equivalent and one cannot always be obtained from the other by using a Legendre transformation. Also, it is not even possible for certain classes of materials to define a Helmholtz potential for bodies belonging to such classes, and for certain other classes to define a Gibbs' potential for bodies belonging to them. The Helmholtz potential formulation has been shown to be capable of modeling generalizations of the Maxwell, Oldroyd-B, Burgers' models as well as models that can be cast within the context of the conformation tensor. These models can also describe the evolution of the anisotropy of such materials during the deformation process. The Gibbs' potential formulation is particularly well suited to the development of models wherein the material moduli that characterize the body are dependent on the invariants of the stress. Thus, such models can be used to describe bodies whose material moduli depend on the mean normal stress and could be very useful in characterizing geological materials. Such a framework would also be particularly relevant to describing the problem of compaction of asphalt concrete as the material property of the compacted body would depend on the mean normal stress which effects the compaction.