Nonlocal damage formulation with evolving internal length: the Eikonal nonlocal approach

International audienceThe proposed contribution presents and investigates the numerical properties of a Eikonal Non-local (ENL) continuum damage model. According to this approach, nonlocal interactions between material points are controlled by geodesic distances obtained as solutions of an isotropic time-independent Eikonal equation with a damage dependent metric function. Nonlocal interactions in two-dimensional damaged domains are illustrated first. A numerical formulation for modeling damage dependent non-local interactions within mechanical computations is presented then. It is obtained by using a Fast-Marching Method for updating damage dependent nonlocal interactions throughout the strain localization process. Numerical results of quasi-static simulations involving the failure of quasi-brittle materials in isotropic media are presented. Regularization properties of the proposed model are demonstrated. Furthermore, it is shown that the proposed formulation allows for reducing several parasite effects classically associated with Integral Nonlocal (INL) formulations (damage spreading over large damaged bands, damage diffusion near notches and free-edges, etc)