Pressure And Fluid Driven Fracture Propagation Using Adaptive Phase Field Models

The computational modeling of the formation and growth of the pressurized and fluid-filled fractures in elastic and poroelastic media is difficult with complex fracture topologies. Here we study the phenomenological fracture propagation by approximating the lower-dimensional fracture surface using the phase field function. The major advantages of using phase field modeling for crack propagation are i) it is a fixed-topology approach in which remeshing is avoided, ii) crack propagation and joining path are automatically determined based on energy minimization, and iii) joining and branching of multiple cracks also do not require any additional techniques. Recently, the phase field approach has been widely employed in different applications including hydraulic fracture propagation in petroleum engineering and developed for various software. The numerical discretization in space is based on Galerkin finite elements for displacements and phase-field, and an Enriched Galerkin method is applied for the pressure equation in order to obtain local mass conservation. The constrained optimization problem is handled by using an active set strategy and nonlinear equations are treated with Newton's method. Predictor-corrector dynamic mesh refinement allows capturing more accurate interface of the fractures with a reasonable number of degrees of freedom. Here, several numerical examples including benchmark problems in two and three-dimensional domains and comparisons with some experiments will be presented using the phase field model.