Phase-field modeling of fracture for quasi-brittle materials

This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topol-ogy.Within the computational mechanics community,several studies have treated the issue of modeling fracture using phase fields.Most of these studies have used an approach that implies the lack of a damage threshold.We herein explore an alternative model that includes a damage threshold and study how it compares with the most popular approach.The formulation is systematically explained within a rigorous variational framework.Subsequently,we present the corresponding three-dimensional finite element discretization that leads to a straightforward numerical implementation.Benchmark simulations in two dimensions and three dimensions are then presented.The results show that while an elastic stage and a damage threshold are ensured by the present model,good agreement with the results reported in the literature can be obtained,where such features are generally absent.