Phase‐Field Models for the Failure of Anisotropic Continua

Hüsnü Dal, Osman Gültekin, Funda Aksu Denli, Gerhard Holzapfel

Research output: Chapter in Book/Report/Conference proceedingConference paper


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.
Original languageEnglish
Title of host publicationProceedings in Applied Mathematics & Mechanics
Number of pages4
Publication statusPublished - Dec 2017
Event88th Annual Meeting of the International Association of Applied Mathematics and Mechanics: GAMM 2017 - Weimar, Germany
Duration: 6 Mar 201710 Mar 2017


Conference88th Annual Meeting of the International Association of Applied Mathematics and Mechanics
Abbreviated titleGAMM
Internet address

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