Force theory for multiphase bodies

Abstract

We present a framework for the study of bodies wherein the deformation gradient may suffer a jump across an evolving nonmaterial interface. To formulate the kinematics relevant to such a situation, we use a global approach in which the configuration space has the structure of an infinite dimensional bundle. We show that a force, defined as an element of the cotangent bundle of the configuration manifold, may be represented by bulk and interfacial stress measures. The invariant decomposition of that force into bulk and interfacial components is discussed and we show that, in the case where the stress measures representing the force are given in terms of smooth densities, such a decomposition is determined by the average stress on the interface.