  We propose a new direction-dependent model for the unilateral constraint
involved in the phase field approach to fracture and also in the continuous
damage mechanics models. The construction of this phase field model is informed
by micromechanical modeling through the homogenization theory, where the
representative volume element (RVE) has a planar crack in the center. The
proposed model is made closely match the response of the RVE, including the
frictionless self-contact condition. This homogenization approach allows to
identify a direction-dependent phase field model with the tension-compression
split obtained from cracked microstructures. One important feature of the
proposed model is that unlike most other models, the material degradation is
consistently determined without artificial assumptions or ad hoc parameters
with no physical interpretation, thus, a more realistic modeling is resulted.
With standard tests such as uniaxial loadings, three-point bending, simple
shear, and through-crack tests, the proposed model predicts reasonable crack
paths. Moreover, with the RVE response as a benchmark, the proposed model gives
rise to an accurate stress-strain curve under shear loads, more accurate than
most existing models.
