The co-divergence of vector valued currents

In the context of stress theory of the mechanics of continuous media, a generalization of the boundary operator for de Rham currents|the co-divergence operator - is introduced. While the boundary operator of de Rham's theory applies to real valued currents, the co-divergence operator acts on vector valued currents, i.e., functionals dual to differential forms valued in a vector bundle. From the point of view of continuum mechanics, the framework presented here allows for the formulation of the principal notions of continuum mechanics on a manifold that does not have a Riemannian metric or a connection while at the same time allowing irregular bodies and velocity fields.