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 …

This paper presents an overview of the theories and computer implementation aspects of
phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches …

Motivated by the successful implementation of the phase-field method (PFM) to simulate
complicated fracture patterns at moderate computational costs in solid materials, many …

Being able to model complex nucleation, propagation, branching and merging of cracks in
solids within a unified framework, the classical phase-field models for brittle fracture fail in …

Being one of the most promising candidates for the modeling of localized failure in solids, so
far the phase-field method has been applied only to brittle fracture with very few exceptions …

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 …

The phase-field model (PFM) represents the crack geometry in a diffusive way without
introducing sharp discontinuities. This feature enables PFM to effectively model crack …

This work outlines a rigorous variational-based framework for the phase field modeling of
ductile fracture in elastic–plastic solids undergoing large strains. The phase field approach …

This work presents a generalization of recently developed continuum phase field models for
brittle fracture towards fully coupled thermo-mechanical and multi-physics problems at large …

This work presents a generalization of recently developed continuum phase field models
from brittle to ductile fracture coupled with thermo-plasticity at finite strains. It uses a …