Inserted: 18 feb 2021
Last Updated: 18 feb 2021
Links: Link to Arxiv
Energy minimality selects among possible configurations of a continuous body with and without cracks those compatible with assigned boundary conditions of Dirichlet-type. Crack paths are described in terms of curvature varifolds so that we consider both "phase" (cracked or non-cracked) and crack orientation. The energy considered is gradient polyconvex: it accounts for relative variations of second-neighbor surfaces and pressure-confinement effects. We prove existence of minimizers for such an energy. They are pairs of deformations and varifolds. The former ones are taken to be $SBV$ maps satisfying an impenetrability condition. Their jump set is constrained to be in the varifold support.
Keywords: calculus of variations, microstructures, varifolds, shells, fracture, ground states