On the notion of the stress tensor associated with \({\mathbb{R}}^ n\)- invariant constitutive laws admitting integral representations (Q757918)

By an \({\mathbb{R}}^ n\)-invariant constitutive law F we mean a smooth \({\mathbb{R}}^ n\)-invariant one form on the Fréchet manifold \(E(M,{\mathbb{R}}^ n)\) of all Euclidean smooth embeddings of a compact manifold M. Associated with it are a natural integrable \({\mathbb{R}}^ n\)- valued one form and a natural two tensor, both embedding dependent, provided F is induced by a one form \(\tilde F\) on \(E(M,{\mathbb{R}}^ n)/{\mathbb{R}}^ n\) and \(\tilde F\) admits an integral representation. This two tensor plays the role of the stress tensor in elasticity theory.