KINEMATICS AND THEORY OF FORCES FOR NONMATERIAL INTERFACES

We present a framework for the study of bodies that contains evolving nonmaterial interfaces. Although analogs of material points and sub-bodies do not exist for such interfaces, we are able to construct a kinematic structure that allows the definition of an interfacial configuration. Equipping the collection of all such configurations, the interfacial configuration space, with the structure of an infinite-dimensional manifold leads to the definition of generalized velocities and forces as elements of the tangent and cotangent bundles of that space. A representation theorem then yields a non-classical force system that arises in recent continuum theories for the study of coherent phase transitions. Associating the underlying body with a particular reference configuration, we find, further, that the elements of that force system are subject to a balance that is also imposed in such theories.