Abstract

As a model for the energy of a brittle elastic body we consider an integral functional consisting of two parts: a volume one which is quadratic in the strain, and a surface part, which is concentrated along the fractures and whose density depends on the jump part of the strain. We study the problem of the lower semicontinuous envelope of such a functional under the assumptions that the surface energy density is positively homogeneous of degree one and that additional geometrical constraints, such as a shearing condition or a normal detachement condition, are imposed on the fractures