Effective moduli of an elastic solid weakened by a parallel array of microcracks

The model about parallel microcracks is used to develop the anisotropic damage theory. An elastic body weakened by parallel microcracks is studied based on the average field theory when the boundary conditions imposed on the RVE meet the Hill condition. It is shown that such a damaged anisotropic elastic body has only 6 independent elastic constants. Besides two elastic constants of the original isotropic matrix there are four elastic constants related to the damage, among them three describe the reduction of the effective elastic constants, and one describe the damage induced tension-shear coupling. After that, an infinite solid containing a doubly periodic array of cracks is analyzed based on the unit cell model and the finite element method. The numerical results reveal that the tension-shear coupling coefficients is much smaller than the other elastic constants for an elastic body with a general doubly periodic array of cracks, and the variation of the in-plane and out-plane shear moduli with the cracks array parameters changing are not the same.