From diffuse damage to strain localization from an Eikonal Non-Local (ENL) Continuum Damage model with evolving internal length

Abstract

International audienc

Damage-to-fracture transition through an Eikonal Non-Local (ENL) continuum damage formulation with embedded strong discontinuities

“…Once this condition is achieved, the global response corresponds to the one obtained using a local damage model, and a residual dependence on the mesh size is observed. The same kind of response was found by [5]. In other words, the residual energy still available in the weakened finite element during the localization phase can only be dissipated in a local manner.…”

“…During the first stages of the damaging process, the behavior of the material follows equations (4) and (5). The damage-to-fracture transition time (at x 0 ∈ Ω) is arbitrarily chosen as the time when D(x 0 ) reaches a critical damage value D cr .…”

“…In this case, the field of geodesic distances is a solution of an eikonal equation in which the metric is damage dependent. Rastiello et al [5] have recently shown that this formulation allows avoiding diffusion of the damage zone observed for the INL for-mulation. Regularization properties are preserved up to a high level of damage.…”

Discontinuity-scale path-following methods for the embedded discontinuity finite element modeling of failure in solids

“…These techniques were successfully applied to non-linear finite element simulations where material nonlinearities were represented using continuum damage mechanics models [13,18], phase-field formulations [14], Thick Level-Set (TLS) damage models [19]. Path-following methods were also used in strong discontinuity simulations, where cracks were modeled using zero-thickness interface finite elements [20,13,17], in the eXtended Finite Element Method (X-FEM) [21] and in the Embedded Finite Element Method (E-FEM) [22,23,24].…”

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

“…Attention is focused on "artificially" damaged domains, in order to put into evidence some key features of the Eikonal Non-Local formulation. A non-intrusive (or less intrusive as possible) numerical formulation [6] for modeling damage dependent nonlocal interactions within mechanical computations is presented then. It is obtained by coupling Fast-Marching [5] algorithms for computing interaction distances and a standard Finite Element (FE) procedure for solving the quasi-static equilibrium equations.…”