Variational phase field model for brittle fracture : insights on dynamic crack branching and propagation in heterogeneous media
Résumé
Simulating crack nucleation and propagation remains a challenging problematic because of the complexity of crack patterns observed in fracture mechanics experiments. Whereas some numerical methods aim at explicitly tracking the crack front evolution, an interesting alternative is offered by continuous approaches of brittle fracture which consist in representing the crack topology using a continuous field varying from 0 (sound material) to 1 (fully cracked material) accross an internal length scale. This « phase field » approach benefits from a variational framework, strongly related to gradient damage models, and can be seen as a regularization of the variational approach to fracture developed by Francfort and Marigo in 1998. Moreover, it does not require any a priori knowledge of the crack path or topology, its evolution being driven only by energy minimization.
Using such an approach combined to a finite-element discretization, the present work aims at providing some insights on crack propagation in a dynamic context. More specifically, crack branching (splitting of a single crack in two or more cracks) is a characteristic phenomenon of dynamic brittle fracture which still lacks a sound theoretical explanation. Numerical simulations will help us better understand some aspects of the branching phenomenon, especially the role played by material heterogeneities in the onset or delay of crack branching.