Discontinuous Galerkin Method in Modeling Materials with Micro-cracks

We analyze wave propagation in heterogeneous brittle materials modeled by a linear elastic body with micro-cracks. The problem is nonlinear due to the boundary conditions on the cracks, such as non-penetration and friction. A numerical upscaling homogenization technique and a discontinuous Galerkin space discretization method are applied to find the effective properties of the damaged material. The wave propagation (speed, amplitude and pulse length) of micro-cracked materials in configurations of varying complexity is studied. While theoretical and numerical wave velocities are found to be very close for small values of the crack density parameter, large values exhibit remarkable differences. Furthermore, we observe that amplitude and speed of the transmitted (damaged) wave are affected by its length when it is close to the length of the micro-cracks.