Notes on stresses for manifolds

The geometric structure of stress theory on differentiable manifolds is considered. Mechanics is assumed to take place on an m-dimensional and no additional metric or parallelism structure is assumed. Two different approaches are described. The first is a generalisation of the traditional Cauchy approach where the resulting stresses are represented mathematically as vector valued (m - 1)-forms. The second approach is variational and stresses are represented by densities valued in the dual of the first jet bundle. It is shown how a variational stress induces a Cauchy stress.