The Divergence of Stress and the Principle of Virtual Power on Manifolds

Abstract

Stresses on manifolds may be introduced from two diflerent points of view. For an m-dimensional material universe, the variational approach regards stresses as fields that associate m-forms, the power densities, with the first jets of generalized velocity fields. In the second approach, the Cauchy approach, stresses are covector valued (m - 1)-forms whose odd restrictions to the the boundary of bodies give the surface forces on them. The relation between the two approaches is studied for general manifolds that are not equipped with a connection.