Metric Independent Analysis of Second Order Stresses

Abstract: 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, $J^{1}(J^{1}W)$, 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.