Ioan Ionescu
Sorbonne Paris Nord University, France

One of the still misunderstood problem remains the behavior of brittle materials (as ceramics) just after fragmentation. Two different types of mechanical models to describe damage in ceramics are considered. The first one is a micro-mechanics based damage model where damage is introduced through a physical parameter. During the damage process the mechanical model loses its isotropy and its homogeneity but the geometric homogeneity is preserved. In the second one damage is introduced by the presence of micro-cracks in an isotropic and homogeneous elastic solid. This geometric heterogeneity induces a loss of isotropy and of homogeneity. Both models take into account the physical reality, where geometric and material heterogeneities are present. For both models we have used a discontinuous Galerkin (DG) numerical scheme, which ensures an efficient parallelization, with a leapfrog scheme for the time discretization and an Exact-Upwind-type choice of the flux. In the second model the main focus lies on the contact conditions at crack surfaces (including crack opening and closure and stick-and- slip with Coulomb friction). Here the interfacial numerical flux is obtained by solving a non-linear and non-smooth system associated to the boundary conditions. We have done some specific numerical simulations on wave propagation in a damaged ceramics us- ing both models. The geometry and the boundary conditions of the numerical simulations were chosen to correspond to some experimental settings.