Finite Element Modelling of 2D Brittle Fracture: The Phase-Field Approach

The prevention of fracture-induced failure is a major constraint in engineering design, and numerical simulations of fracture processes often play a key role in design decisions. Although huge efforts have been made to develop novel and more accurate models of fracture and an enormous progress has been achieved in the recent years, the development of an adequate scheme for the numerical simulation of crack initiation and propagation is still a significant challenge for the scientific community. The goal of this paper is twofold: (i) to give an overview of current numerical methods available in the literature for the analysis of brittle fracture problems; (ii) to present a finite element phase-field scheme for the analysis of brittle fracture problems. This scheme relies on recently developed strategies for incorporating an additional phase-field to account for fracture. The spatial finite element discretization is formulated by means of the classical Galerkin method, whereas an implicit Euler method with adaptive time-stepping is adopted for the temporal discretization. To demonstrate the capabilities of the model, some numerical experiments are modelled.