A numerical study of a nonlocal model of damage propagation under chemical aggression

We introduce a differential model to study damage accumulation processes in presence of chemical reactions. The influence of micro-structure leads to a nonlinear parabolic system characterized by the presence of a characteristic length. Here, we first present an analytical description of the qualitative behavior of solutions which blow-up in finite time. Numerical simulations are given to describe the shape of solutions near the rupture time and the influence of the chemical reagents. Like in the non reactive model, the failure of the material occurs in a region of positive measure, due to the diffusive effects of the micro-structure, although some localization phenomena are observed. Moreover, if we increase the chemical concentration beyond a given threshold, which depends on the specific conditions of the material, we observe a strong acceleration in the damage process.