This paper presents an overview of the theories and computer implementation aspects of
phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches …

Motivated by the successful implementation of the phase-field method (PFM) to simulate
complicated fracture patterns at moderate computational costs in solid materials, many …

Naturally fractured rock mass is highly inhomogeneous and contains geological
discontinuities at various length scales. Hydraulic fracture stimulation in such a medium …

This paper proposes a phase field model for fracture in poroelastic media. The porous
medium is modeled based on the classical Biot poroelasticity theory and the fracture …

A phase field model for fluid-driven dynamic crack propagation in poroelastic media is
proposed. Therefore, classical Biot poroelasticity theory is applied in the porous medium …

This work presents phase field fracture modeling in heterogeneous porous media. We
develop robust and efficient numerical algorithms for pressure-driven and fluid-driven …

The effects of rock inherent heterogeneity and grain size on hydraulic fracture initiation and
propagation for different propagation regimes are investigated through two dimensional …

In the hydraulic fracturing of natural rocks, understanding and predicting crack penetrations
into the neighboring layers is crucial and relevant in terms of cost-efficiency in engineering …

Rigorous coupling of fracture–porous medium fluid flow and topologically complex fracture
propagation is of great scientific interest in geotechnical and biomechanical applications. In …

Phase-field approaches to fracture based on energy minimization principles have been
rapidly gaining popularity in recent years, and are particularly well-suited for simulating …