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 …

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 …

The present paper aims at modeling complex fracture phenomena where different damaging
mechanisms are involved. For this purpose, the standard one-variable phase-field/gradient …

The critical energy release rates for mode I and II fracture for rock-like materials are usually
different. In this paper, a modified phase-field model is proposed for simulating mixed mode …

Irreversible evolution is one of the central concepts as well as implementation challenges of
both the variational approach to fracture by Francfort and Marigo (1998) and its regularized …

The phase-field model has been attracting considerable attention due to its capability of
capturing complex crack propagations without mesh dependence. However, its validation …

In this article, we focus on the validation of Francfort and Marigo's variational approach to
fracture based on some classical fracture experiments. We show that this approach can be …

We introduce a class of models based on near crack tip degradation of materials that can
account for fracture growth under cyclic loads below the Griffith threshold. We incorporate …

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the
phase-field approach for fracture by modeling the crack as a diffusive object being described …

These lecture notes address the main challenging computational aspects of phase-field
modeling of brittle fracture. We focus, in particular, on the irreversibility constraint and the …