Crack Occurrence in Bodies with Gradient Polyconvex Energies

In a set of infinitely many reference configurations differing from chosen fit region $${\mathscr {B}}$$ in the three-dimensional space and each other only by possible crack paths, parameterized special measures, namely curvature varifolds, energy minimality selects among continuous body those that are compatible with assigned boundary conditions Dirichlet-type. The use varifolds allows us to consider both “material phase" (cracked or non-cracked) orientation. considered is gradient polyconvex: it accounts for relative variations second-neighbor surfaces pressure-confinement effects. We prove existence minimizers such an energy. They pairs deformations varifolds. former ones taken be SBV maps satisfying impenetrability condition. Their jump constrained varifold support.