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 …

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 …

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 …

The phase field paradigm, in combination with a suitable variational structure, has opened a
path for using Griffith's energy balance to predict the fracture of solids. These so-called …

We present a gradient-based theoretical framework for predicting hydrogen assisted fracture
in elastic-plastic solids. The novelty of the model lies in the combination of:(i) stress-assisted …

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 …

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 …

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 …

We propose a new variational fatigue phase-field model. The basic idea of the model is to let
the fracture energy decrease as a suitably defined accumulated strain measure increases …

Phase field fracture models have demonstrated great capacities in simulating crack
nucleation, propagation, branching, and joining in brittle and ductile materials subjected to …