Phase‐Field Models for the Failure of Anisotropic Continua

Phase‐Field Models for the Failure of Anisotropic Continua This study presents a phase‐field approach for an anisotropic continuum to model fracture of biological tissues and fiber‐reinforced composites. We start with the continuous formulation of the variational principle for the multi‐field problem manifested through the deformation map and the crack phase‐field at finite strains which leads to the Euler–Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the anisotropic crack phase‐field and the balance of linear momentum. In addition, we propose a novel energy‐based anisotropic failure criterion which regulates the evolution of the crack phase‐field. The coupled problem is solved using a one‐pass operator‐splitting algorithm composed of a mechanical predictor step and a crack evolution step. Representative numerical examples are devised for crack initiation and propagation in carbon‐fiber‐reinforced polymerg composites. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results qualitatively capture the effect of anisotropy in stiffness and strength. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Phase‐Field Models for the Failure of Anisotropic Continua

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710027
Publisher site
See Article on Publisher Site

Abstract

This study presents a phase‐field approach for an anisotropic continuum to model fracture of biological tissues and fiber‐reinforced composites. We start with the continuous formulation of the variational principle for the multi‐field problem manifested through the deformation map and the crack phase‐field at finite strains which leads to the Euler–Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the anisotropic crack phase‐field and the balance of linear momentum. In addition, we propose a novel energy‐based anisotropic failure criterion which regulates the evolution of the crack phase‐field. The coupled problem is solved using a one‐pass operator‐splitting algorithm composed of a mechanical predictor step and a crack evolution step. Representative numerical examples are devised for crack initiation and propagation in carbon‐fiber‐reinforced polymerg composites. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results qualitatively capture the effect of anisotropy in stiffness and strength. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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