Existence of energetic solutions for rate–independent delamination models on domains with polyhedral interfaces

A model for a composite of elastic solids exposed to rate independent delamination processes along prescribed interfaces is studied. The composite is given as the disjoint union of open, convex polyhedra, whose boundaries are described by a Voronoi tessellation, defining the interfaces between the different material components. For this setup suitable Poincaré and Korn inequalities for Sobolev functions with jumps along prescribed interfaces are proved. Based on this, the existence of solutions for the delamination model in the framework of energetic solutions of rate-independent processes is established.