Non-local interactions across damaged bands and near notches or free-edges in isotropic Eikonal Non-Local (ENL) damage models

International audienceIntegral non-local (INL) formulations on the internal variables of the constitutive model [1] are widely used to regularize Continuum Damage computations, in the presence of stress softening for instance. According to this approach the thermodynamic variable driving the damage evolution process at a given material point is computed by weighted averaging of the corresponding local field over the entire domain. Averaging is performed through a non-local weighting function, such that the higher the Cartesian distance between two material points, the lower is their interaction. A main drawback of this assumption consists, however, in nonphysical interactions between material points across damaged bands, cracks and holes. From a numerical viewpoint, this induces some parasite effects, such as damage spreading over a large damaged band, damage diffusion near notches and free-edges, etc. Enhancements of the initial methods were proposed by allowing non-local interactions to evolve depending on mechanical fields (e.g. damage, stress, strain). The Eikonal Non-Local (ENL) formulation [2, 3] provides a novel interpretation of damage dependent evolving non-local interactions. According to this approach, one considers that damage induces a curvature of the Riemannian space in which interaction distances are computed. As a consequence, non-local interactions between material points are controlled by geodesic distances approximating the viscosity solution of an isotropic time-independent Eikonal equation with a damage dependent Riemannian metric function. Geodesic distances are then used to define the kernel of weighting function to be used in integral non-local averaging. This mathematical and physical framework allows for directly modeling evolving interactions throughout the damage process, from damage growth to strain local-ization. In this contribution, a simple isotropic ENL damage model and its numerical implementation [3] are presented first. Two-dimensional strain localization problems are then simulated in order to present the main features of the proposed formulation. Attention is mainly focused on non-local interactions across damaged bands and near notches and/or free-edges, to show that parasite effects classically associated with standard INL formulations are avoided, or at least strongly reduced