Along with horizontal drilling techniques, multi-stage hydraulic fracturing has improved shale
gas production significantly in past decades. In order to understand the mechanism of …

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 …

Phase-field models, sometimes referred to as gradient damage or smeared crack models,
are widely used methods for the numerical simulation of crack propagation in brittle …

We investigate the potential of quasi-Newton methods in facilitating convergence of
monolithic solution schemes for phase field fracture modelling. Several paradigmatic …

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 …

In this paper, we propose an explicit phase field model for dynamic brittle fracture. The
mechanical field is integrated with a Verlet-velocity scheme, while the phase field is …

The prediction of fluid-and moisture-driven crack propagation in deforming porous media
has achieved increasing interest in recent years, in particular with regard to the modeling of …

In this paper, we consider phase-field based fracture propagation in elastic media. The main
purpose is the development of a robust and efficient numerical scheme. To enforce crack …