The Energy of a One-Dimensional Structured Deformation

Abstract

Starting from an assumed expression for the energy of a simple deformation, a representation formula for the energy of a one-dimensional structured deformation is obtained. If w and 0 denote the bulk and the interfacial energy density for a simple deformation, the corresponding densities for a structured deformation are determined by the lower semicontinuous and convex envelope of w and by the subadditive envelope of 0. This result holds under a specific type of convergence assumed for approximating sequences of simple deformations; as discussed briefly in the final remarks, other physically meaningful notions of convergence may lead to different expressions for the energy.