Notes on stress measures on bodies with corners

In a global, non-linear, geometric formulation of force and stress theory for continuum mechanics, a body is modeled as a compact manifold with corners and the configuration space consists of all C¹-embeddings of the body in a physical space manifold. A Force at a given configuration is a linear functional on the space of C¹-generalized velocities, that is, a linear functional on a space of sections of a vector bundle over the body. Stresses are introduced through a representation theorem as measures, valued on the dual of the first jet bundle, which represent forces. This paper considers various properties of such stress measures. In particular, we discuss regularization of forces and stresses, and study the relation between forces and stresses in the non-smooth case from a new point of view.