A Variational Problem in the Mechanics of Complex Materials

We analyze the possible nucleation of cracked surfaces in materials in which changes in the material texture have a prominent influence on the macroscopic mechanical behavior. The geometry of crack patterns is described by means of stratified families of curvature varifolds with boundary. Possible non-local actions of the microstructures are accounted for. We prove existence of ground states of the energy in terms of deformation, descriptors of the microstructure and varifolds.