International audienc

The numerical simulation of two-dimensional fracture processes of quasi-brittle materials by means of the Embedded Finite Element Method is dealt with. Attention is paid to the coupling with the global crack-tracking strategy, which has been proposed in the literature in the form of a heat conduction-like problem. It turns out that the stiffness-like matrix associated with this formulation is singular and a numerical perturbation has to be intro-duced in order to overcome the ill-posedness of the problem. The dependence of the solu-tion on this parameter may represent a limitation for the global tracking approach. Furthermore, it is found that if the root of each discontinuity is not updated during an incremental analysis, a loss of continuity of the crack path may appear when principal stress directions rotate. This paper aims to provide a solution to the aforementioned issues. An alternative mathematical formulation of the problem is thus given in terms of Navier-Stokes equations, linking the diffusive contribution to a characteristic mesh length. Additionally, a modified cracktracking algorithm, considering the evolution of the root for the identification of the crack path, is proposed. The numerical assessment of the pro-posed tracking strategy is reported by means of benchmark tests at the structural level.