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 …

Fracture is one of the most commonly encountered failure modes of engineering materials
and structures. Prevention of cracking-induced failure is, therefore, a major concern in …

In this contribution we address the issue of efficient finite element treatment for phase-field
modeling of brittle fracture. We start by providing an overview of the existing quasi-static and …

Compressive-shear fracture is commonly observed in rock-like materials. However, this
fracture type cannot be captured by current phase field models (PFMs), which have been …

Unlike the description of cracks as sharp surfaces which requires different criteria to predict
the onset of crack propagation, the direction of crack growth, possible crack branching, and …

The phase-field method has become an important and extremely versatile technique for
simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface …

The phase-field model for fractures regularizes crack diffusion using a length-scale
parameter. The displacement fields and the phase-field in a coupled system can be solved …

Different fracture patterns can be observed because of different material properties, even the
geometry and loading are the same. However, most of the known phase-field fracture …

New perspectives on the phase field approach in modeling deformation and fracture at the
fundamental defect level are reviewed. When applied at sub-angstrom length scales the …

The formulation of a phase-field continuum theory for brittle fracture in elastic–plastic solids
and its computational implementation are presented in this contribution. The theory is based …