A FEniCS implementation of the phase field method for quasi-static brittle fracture

In the recent years, the phase field method for simulating fracture problems has received considerable attention. This is due to the salient features of the method: 1) it can be incorporated into any conventional finite element software; 2) has a scalar damage variable is used to represent the discontinuous surface implicitly and 3) the crack initiation and subsequent propagation and branching are treated with less complexity. Within this framework, the linear momentum equations are coupled with the diffusion type equation, which describes the evolution of the damage variable. The coupled nonlinear system of partial differential equations are solved in a ‘staggered’ approach. The present work discusses the implementation of the phase field method for brittle fracture within the open-source finite element software, FEniCS. The FEniCS provides a framework for the automated solutions of the partial differential equations. The details of the implementation which forms the core of the analysis are presented. The implementation is validated by solving a few benchmark problems and comparing the results with the open literature.