Advances in Applied Mechanics

4.2 Cauchy's theorem for microstructural contact actions

We assume that τ is a function of the point x and the normal n to $\partial \mathfrak{b}$ at all points where the normal itself is uniquely defined and at every instant. In other words, we presume the validity of Cauchy's postulate for the microstructural contact actions. A question is then whether we can prove the Cauchy theorem for τ.

A proof is given in Capriz and Virga (1990), but there the microstructure is represented in a manifold embedded into a linear space, with undoubted advantages. Here we want to maintain the representation of the microstructure in a manifold as abstract as possible, avoiding ...