A fourth-order degradation tensor for an anisotropic damage phase-field model

This work proposes a thermodynamically consistent phase-field model for anisotropic brittle material under the hypotheses of plane stress, small deformation and constant temperature. The model is derived from the principle of virtual power, the first and second laws of thermodynamics in the form of the Clausius-Duhem inequality. The degradation effect on the material behavior is given by a fourth-order degradation tensor introduced as an internal variable that evolves according to the current strain state rather than the conventional scalar degradation function of phase-field models. Therefore, local anisotropy can be induced, changing the material mechanical behavior differently in all directions organically. The proposed degradation tensor is defined in the global coordinate system and therefore is sensitive to any change in the principal directions of the strain and stress states. To demonstrate the model’s capability of representing damage in isotropic and transversely isotropic materials, some benchmark examples were carried out and the evolution of the damage components was analyzed.