Phase-field method is a density-based computational method at the mesoscale for modeling
and predicting the temporal microstructure and property evolution during materials …

Rockburst is becoming a huge challenge for the utilization of deep underground space.
Extensive efforts have been devoted to investigating the rockburst behavior and mechanism …

This document presents comprehensive historical accounts on the developments of finite
element methods (FEM) since 1941, with a specific emphasis on developments related to …

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 …

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 …

Phase-field models, sometimes referred to as gradient damage or smeared crack models,
are widely used methods for the numerical simulation of crack propagation in brittle …

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 …

Based upon advances in theoretical algorithms, modeling and simulations, and computer
technologies, the rational design of materials, cells, devices, and packs in the field of lithium …