Mechanics Based on an Objective Power Functional

Abstract

During the recent years, the interest in non-classical material theories has significantly grown, due to the fact that classical theories can not describe certain effects, in principle. In particular, higher order gradient theories have turned out to become a promising remedy, since they open the way to conceptually new formats wide enough to include, e. g., internal length scales.

The inclusion of higher deformation gradients raises many questions. One expects the parallel existence of higher order stress tensors, for which the balances and boundary conditions have to be generalized. This generalization, however, is by no means trivial nor unique. In the present paper, these concepts are derived by posing invariance requirements upon a general principle of virtual power, as a linear and continuous extension of the balance of work. By such a procedure, a catalogue of different, but essentially equivalent load systems and balances can be obtained, which can be further particularised for specific materials.