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 …

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

We present a generalised phase field-based formulation for predicting fatigue crack growth
in metals. The theoretical framework aims at covering a wide range of material behaviour …

A novel variational framework to model the fatigue behavior of brittle materials based on a
phase-field approach to fracture is presented. The standard regularized free energy …

Twenty years in since their introduction, it is now plain that the regularized formulations
dubbed as phase-field of the variational theory of brittle fracture of Francfort and Marigo …

We present a generalised phase field formulation for predicting high-cycle fatigue in metals.
Different fatigue degradation functions are presented, together with new damage …

We present a new phase field framework for modelling fracture and fatigue in Shape
Memory Alloys (SMAs). The constitutive model captures the superelastic behaviour of SMAs …

Phase-field method, as a powerful and popular approach to predict the mesoscale
microstructure evolution in various materials science, provides a bridge from atomic-scale …

In this work, the phase-field approach to fracture is extended to model fatigue failure in high-
and low-cycle regime. The fracture energy degradation due to the repeated externally …