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

The phase-field method has gained much attention as a novel method to simulate fracture
due to its straightforward way allowing to cover crack initiation and propagation without …

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 …

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

In this paper, we present a phase-field method combined with an explicit cycle jump scheme
for simulating low-cycle fatigue fracture in brittle materials in both two and three dimensions …

A phase-field approach was used in order to model the complex mechanisms of fatigue
crack nucleation and growth. This popular method enables a flexible framework that …

Recently, phase field modeling of fatigue fracture has gained a lot of attention from many
researches and studies, since the fatigue damage of structures is a crucial issue in …

In this paper, a possible extension of Griffith's fracture theory to describe fatigue-induced
crack propagation is proposed. To this end, an energy-based model is presented, taking …

Prediction of the fatigue life of piezoelectric devices and structures is of scientific and
engineering significance. In this work, a phase field model for fatigue fracture in piezoelectric …

A novel FFT-based phase-field fracture framework for modelling fatigue crack initiation and
propagation at the microscale is presented. A damage driving force is defined based on the …