Singular Surfaces in Dipolar Materials and Possible Consequences for Continuum Mechanics

Abstract

In this paper we study the evolutionary behaviour of a propagating singular surface in two types of nonlinear dipolar materials; a compressible inviscid dipolar fluid and an elastic dipolar solid.

The basic theory we use was introduced by Green and Rivlin [l] and from the constitutive theory viewpoint essentially extends classical continuum mechanics by including gradients of the independent variables present in non-polar theories. Gradient type theories were suggested earlier by, for example, Maxwell and by Korteweg, see Truesdell and Noll [2], §125; in particular, Korteweg developed an interesting theory of surface tension by allowing for the possibility of rapidly changing density gradients in an interface. Since in a singular surface quantities such as density and its gradients of various orders may change very rapidly a study of wave motion in multipolar materials may prove of value.