  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 \textquotedblleft 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 the 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.
