We study an elastic compound that is exposed to rate-independent delamination processes along prescribed interfaces. The interfaces are described by convex polyhedra of random geometry. By means of stochastic two-scale homogenization we deduce a macroscopic phase-field model for rate-independent volume damage. This is joint work in progress with Martin Heida (WIAS) and Leon Schütz, supported by the German Research Foundation (DFG) within CRC 1114 Scaling Cascades in Complex Systems, project B09 Materials with Discontinuities on Many Scales and within CRC/TRR 388 Rough Analysis, Stochastic Dynamics & Related Fields, project B09 Mean field theories and scaling limits of nonlinear stochastic evolution systems.