The recently introduced phase-field approach for pressurized fractures in a porous medium offers various attractive computational features for numerical simulations of cracks such as joining, branching, and nonplanar propagation in possibly heterogeneous media. In this paper, the pressurized phase-field framework is extended to fluid-filled fractures in which the pressure is computed from a generalized parabolic diffraction problem. Here, the phase-field variable is used as an indicator function to combine reservoir and fracture pressure. The resulting three-field framework (elasticity, phase field, pressure) is a multiscale problem that is based on the Biot equations. The proposed numerical solution algorithm iteratively decouples the equations using a fixed-stress splitting. The framework is substantiated with several numerical benchmark tests in two and three dimensions.

Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized.