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Phase‐Field Models for the Failure of Anisotropic Continua
Author(s) -
Dal Hüsnü,
Gültekin Osman,
Aksu Denli Funda,
Holzapfel Gerhard A.
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710027
Subject(s) - anisotropy , finite element method , stiffness , field (mathematics) , mechanics , phase (matter) , materials science , fracture (geology) , fracture mechanics , mathematical analysis , mathematics , structural engineering , physics , composite material , engineering , quantum mechanics , pure mathematics
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)