Variational Methods in the Mechanics of Solids

Abstract

Based on invariant variational principles due to Noether, it is possible to derive several conservation theorems of mathematical physics applicable, in principle, for any field theory. These conservation laws, and the resulting so-called path-independent integrals, have proved useful in continuum mechanics and in particular in the theory of elasticity. Several new applications of these conservation theorems will be discussed, including specifically those to elastodynamics, thermoelasticity, porous media, and the experimental determinations of stress intensity factors in fracture mechanics.