Several models have been developed over the last decades to predict cracking behavior, the majority of them using the finite element model (FEM). A crack introduces discontinuities in the displacement field which are not easily implemented in a continuum mechanics framework. Phase-field models introduce a continuous variable that represents the damage in the material which overcomes most of the difficulties previously described due to the energetic description of the phenomenon. Predicting complex crack paths taking into account local induced anisotropy is more difficult. The local degradation may introduce anisotropy in initially isotropic materials or change the original anisotropy of materials. This change in the material properties as a result of crack propagation is called local damage anisotropy. Based on previous works, an anisotropic damage phase-field model was developed in a thermodynamically consistent framework. In the present work, the degradation of the material properties is not given by the composition of a damage variable with any arbitrary degradation function. Instead, the degradation is defined by a fourth-order degradation tensor which is introduced as an internal variable and governed by an evolution law based on thermodynamic considerations. Results for 2D and 3D examples for brittle and ductile materials are presented.