Along with horizontal drilling techniques, multi-stage hydraulic fracturing has improved shale
gas production significantly in past decades. In order to understand the mechanism of …

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 …

Innovations of advanced materials have been at the core of most engineering technologies,
devices and systems. Composite laminates in particular have been extensively employed in …

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 …

Phase-field models have been a topic of much research in recent years. Results have
shown that these models are able to produce complex crack patterns in both two and three …

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 …

In order to model brittle fracture, we have implemented a two and three dimensional phase-
field method in the commercial finite element code Abaqus/Standard. The method is based …

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 …

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 …