Non Interpenetration of Matter for Sbv -deformations of Hyperelastic Brittle Materials

We prove that the Ciarlet-Nečas non-interpenetration of matter condition [9] can be extended to the case of SBV -deformations of hyperelastic brittle materials, and can be taken into account for some variational models in fracture mechanics. In order to formulate such a condition, we define the deformed configuration under an SBV -map by means of the approximately differentiable representative, and we prove some connected stability results under weak convergence. We provide an application to the case of brittle Ogden’s materials.