Phase-field models for the failure of anisotropic continua

Dal, Hüsnü
Aksu Denli, Funda
Holzapfel, Gerhard
This study presents a phase-field approach for an anisotropic continuum to model fracture of biological tissues and fibre-reinforced composites. We start by deriving the regularized crack surface to overcome complexities inherent in sharp crack discontinuities, thereby relaxing the acute crack surface topology into a diffusive one. In fact, the regularized crack surface possesses the property of Gamma-Convergence, i.e. the sharp crack topology is restored with a vanishing length-scale parameter. Next, we deal 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. As an important aspect of the continuum formulation we consider an invariant-based anisotropic constitutive models for single and multiple families of fibers embedded in the ground matrix. 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. Various anisotropic failure criteria are studied. Our preliminary investigations suggest that the novel energy based anisotropic failure criteria presented is superior to stress based criteria existing in the literature. Representative numerical examples are devised for crack initiation and propagation in CFRP composites and rupture in thoracic aorta. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results agree favorably with the experimental findings.
88th Annual Meeting of the International Association of Applied Mathematics and Mechanics, March 6-10, 2017


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Citation Formats
H. Dal, F. Aksu Denli, and G. Holzapfel, “Phase-field models for the failure of anisotropic continua,” presented at the 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics, March 6-10, 2017, Weimar, Germany, 2017, Accessed: 00, 2021. [Online]. Available: