A variationally consistent phase-field anisotropic damage model for fracture

Jian Ying Wu, Vinh Phu Nguyen, Hao Zhou, Yuli Huang

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In the phase-field modeling of fracture in brittle and quasi-brittle solids, it is crucial to represent the asymmetric tensile/compressive material behavior. Existing phase-field models generally adopt either an intuitive split of the free energy density without capturing the crack boundary conditions properly or an ad hoc hybrid formulation at the loss of variational consistency. To address this issue, this work presents a variationally consistent phase-field anisotropic damage model within the framework of the unified phase-field theory for brittle fracture and quasi-brittle failure Wu [1, 2]. Consistent with the variational approach to fracture, the positive/negative projection of the effective stress in energy norm Wu and Cervera [3] is adopted, minimizing the tensile part of the stored energy that drives crack evolution. A rounded-Rankine criterion naturally emerges to realistically characterize localized failure of brittle and quasi-brittle solids, with no need of ad hoc assumptions. A mixed-mode cohesive zone model is recovered upon strain localization, with the involved parameters determined from the analytical solution of a softening bar under constrained stretching. Representative numerical examples show that the proposed model can capture arbitrary cracks propagation in solids independently of the mesh discretization and length scale parameter. Remarkably, the spurious stress locking, which is notoriously accompanied with classical anisotropic damage models, is not exhibited.

Original languageEnglish
Article number112629
Number of pages28
JournalComputer Methods in Applied Mechanics and Engineering
Volume358
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • Anisotropic damage
  • Cohesive zone model
  • Phase-field theory
  • Unilateral effects
  • Variational approach to fracture

Cite this

@article{eda3800fb002492195943d44517df308,
title = "A variationally consistent phase-field anisotropic damage model for fracture",
abstract = "In the phase-field modeling of fracture in brittle and quasi-brittle solids, it is crucial to represent the asymmetric tensile/compressive material behavior. Existing phase-field models generally adopt either an intuitive split of the free energy density without capturing the crack boundary conditions properly or an ad hoc hybrid formulation at the loss of variational consistency. To address this issue, this work presents a variationally consistent phase-field anisotropic damage model within the framework of the unified phase-field theory for brittle fracture and quasi-brittle failure Wu [1, 2]. Consistent with the variational approach to fracture, the positive/negative projection of the effective stress in energy norm Wu and Cervera [3] is adopted, minimizing the tensile part of the stored energy that drives crack evolution. A rounded-Rankine criterion naturally emerges to realistically characterize localized failure of brittle and quasi-brittle solids, with no need of ad hoc assumptions. A mixed-mode cohesive zone model is recovered upon strain localization, with the involved parameters determined from the analytical solution of a softening bar under constrained stretching. Representative numerical examples show that the proposed model can capture arbitrary cracks propagation in solids independently of the mesh discretization and length scale parameter. Remarkably, the spurious stress locking, which is notoriously accompanied with classical anisotropic damage models, is not exhibited.",
keywords = "Anisotropic damage, Cohesive zone model, Phase-field theory, Unilateral effects, Variational approach to fracture",
author = "Wu, {Jian Ying} and Nguyen, {Vinh Phu} and Hao Zhou and Yuli Huang",
year = "2020",
month = "1",
day = "1",
doi = "10.1016/j.cma.2019.112629",
language = "English",
volume = "358",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",

}

A variationally consistent phase-field anisotropic damage model for fracture. / Wu, Jian Ying; Nguyen, Vinh Phu; Zhou, Hao; Huang, Yuli.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 358, 112629, 01.01.2020.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - A variationally consistent phase-field anisotropic damage model for fracture

AU - Wu, Jian Ying

AU - Nguyen, Vinh Phu

AU - Zhou, Hao

AU - Huang, Yuli

PY - 2020/1/1

Y1 - 2020/1/1

N2 - In the phase-field modeling of fracture in brittle and quasi-brittle solids, it is crucial to represent the asymmetric tensile/compressive material behavior. Existing phase-field models generally adopt either an intuitive split of the free energy density without capturing the crack boundary conditions properly or an ad hoc hybrid formulation at the loss of variational consistency. To address this issue, this work presents a variationally consistent phase-field anisotropic damage model within the framework of the unified phase-field theory for brittle fracture and quasi-brittle failure Wu [1, 2]. Consistent with the variational approach to fracture, the positive/negative projection of the effective stress in energy norm Wu and Cervera [3] is adopted, minimizing the tensile part of the stored energy that drives crack evolution. A rounded-Rankine criterion naturally emerges to realistically characterize localized failure of brittle and quasi-brittle solids, with no need of ad hoc assumptions. A mixed-mode cohesive zone model is recovered upon strain localization, with the involved parameters determined from the analytical solution of a softening bar under constrained stretching. Representative numerical examples show that the proposed model can capture arbitrary cracks propagation in solids independently of the mesh discretization and length scale parameter. Remarkably, the spurious stress locking, which is notoriously accompanied with classical anisotropic damage models, is not exhibited.

AB - In the phase-field modeling of fracture in brittle and quasi-brittle solids, it is crucial to represent the asymmetric tensile/compressive material behavior. Existing phase-field models generally adopt either an intuitive split of the free energy density without capturing the crack boundary conditions properly or an ad hoc hybrid formulation at the loss of variational consistency. To address this issue, this work presents a variationally consistent phase-field anisotropic damage model within the framework of the unified phase-field theory for brittle fracture and quasi-brittle failure Wu [1, 2]. Consistent with the variational approach to fracture, the positive/negative projection of the effective stress in energy norm Wu and Cervera [3] is adopted, minimizing the tensile part of the stored energy that drives crack evolution. A rounded-Rankine criterion naturally emerges to realistically characterize localized failure of brittle and quasi-brittle solids, with no need of ad hoc assumptions. A mixed-mode cohesive zone model is recovered upon strain localization, with the involved parameters determined from the analytical solution of a softening bar under constrained stretching. Representative numerical examples show that the proposed model can capture arbitrary cracks propagation in solids independently of the mesh discretization and length scale parameter. Remarkably, the spurious stress locking, which is notoriously accompanied with classical anisotropic damage models, is not exhibited.

KW - Anisotropic damage

KW - Cohesive zone model

KW - Phase-field theory

KW - Unilateral effects

KW - Variational approach to fracture

UR - http://www.scopus.com/inward/record.url?scp=85072582270&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2019.112629

DO - 10.1016/j.cma.2019.112629

M3 - Article

VL - 358

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 112629

ER -