The co-divergence of vector valued currents

Abstract

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