On calculation of effective elastic properties of materials with cracks

A simple approach for calculation of anisotropic effective elastic properties of cracked materials is presented. Square computational domain containing randomly distributed cracks under plane strain conditions is considered. Effective elastic properties are expressed in terms of average displacement discontinuities on cracks in three test problems: uniaxial loading in two orthogonal directions and pure shear. These problems are solved using the displacement discontinuity method. Resulting effective compliances are averaged over realizations with different crack distributions. This approach is employed for calculation of effective elastic properties for two particular crack configurations: (i) one family of parallel cracks and (ii) two families of parallel cracks inclined at angle 30°. Crack densities up to 0.8 are considered. It is shown that for both configurations the effective elastic properties are orthotropic even at large crack densities. Dependencies of Young's moduli on crack density are obtained. At crack densities up to 0.1, the effective properties can be estimated analytically using the noninteraction approximation (NIA). At higher crack densities, the NIA strongly overestimates effective stiffnesses. Quantitative agreement with results obtained in the literature using more sophisticated methods is demonstrated.