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-bo dies do not exist for such interfaces, we are able to construct a kine matic structure that allows the definition Of an interfacial configura tion. Equipping the collection of all such configurations, the interfa cial configuration space, with the structure of an infinite-dimensiona l manifold leads to the definition of generalized velocities and force s as elements of the tangent and cotangent bundles of that space. A re presentation theorem then yields a non-classical force system that ari ses in recent continuum theories for the study of coherent phase trans itions. Associating the underlying body with a particular reference co nfiguration, we find, further, that the elements of that force system are subject to a balance that is also imposed in such theories.