Effective anisotropic compliance relationships for wing-cracked brittle materials under compression

The failure mechanism for brittle materials under compressive loading is generally assumed to be dominated by the development of wing-cracks. Due to the preferential direction of the wing-crack development, material damaged in this mode exhibits damage induced anisotropy and volume dilatancy. The effective compliance of such wing-crack damaged materials is important for developing micromechanics-based constitutive models. This work addresses the scenario of a brittle material with periodically distributed wing-cracks under uniaxial compressive load. Closed form expressions for the instantaneous anisotropic compliance tensor with respect to the key physical parameters of the wing-cracks (the number density of cracks, the pre-existing flaw orientations and flaw sizes, the instantaneous length of wing-cracks, and the friction coefficient on the flaw surfaces) are derived through a kinematic approach. Accordingly, finite element models with perturbing compressive loads and periodic boundary conditions are carried out based on the above ideological wing-crack model, in order to verify and parameterize the analytically-based model. Good agreement is found between the finite element results and the analytical expression.