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 …

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 …

Phase-field models have been a topic of much research in recent years. Results have
shown that these models are able to produce complex crack patterns in both two and three …

Phase-field modeling of brittle fracture in elastic solids is a well-established framework that
overcomes the limitations of the classical Griffith theory in the prediction of crack nucleation …

In contrast to discrete descriptions of fracture, phase-field descriptions do not require
numerical tracking of discontinuities in the displacement field. This greatly reduces …

Phase-field models based on the variational formulation for brittle fracture have recently
been gaining popularity. These models have proven capable of accurately and robustly …

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 …

Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …

Being able to seamlessly deal with complex crack patterns like branching, merging and
even fragmentation, the phase-field model, amongst several alternatives, is promising in the …