This study presents a phase-field approach for an anisotropic continuum to model fracture of biological tissues and fiberreinforced 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.

This study presents a crack phase-field approach for anisotropic continua to model, in particular, fracture of fiber-reinforced matrix composites. Starting with the variational formulation of the multi-field problem of fracture in terms of the deformation and the crack phase fields, the governing equations feature the evolution of the anisotropic crack phase-field and the balance of linear momentum, presented for finite and small strains. A recently proposed energy-based anisotropic failure criterion is incorporated into the model with a constitutive threshold function regulating the crack initiation in regard to the matrix and the fibers in a superposed framework. Representative numerical examples are shown for the crack initiation and propagation in unidirectional fiber-reinforced polymer composites under Mode-I, Mode-II and mixed-mode bending. Model parameters are obtained by fitting to sets of experimental data. The associated finite element results are able to capture anisotropic crack initiation and growth in unidirectional fiber-reinforced composite laminates.

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