Metric Independent Analysis of Second Order Stresses

A metric independent geometric analysis of second order stresses in continuum mechanics is presented. For a vector bundle W over the n-dimensional space manifold, the value of a second order stress at a point x in space is represented mathematically by a linear mapping between the second jet space of W at x and the space of n-alternating tensors at x. While only limited analysis can be performed on second order stresses as such, they may be represented by non-holonomic stresses, whose values are linear mapping defined on the iterated jet bundle, J1(J1W), and for which an iterated analysis for first order stresses may be performed. As expected, we obtain the surface interactions on the boundaries of regions in space.