A numerical damage model for initially anisotropic materials

Significant progresses have been realized during the last decades on both macroscopic and micro-mechanical modeling of induced damage in brittle materials. Most damage models developed so far were devoted to initially isotropic materials. This work is devoted to modeling of induced damage in an initially anisotropic material. A numerical micro-mechanical damage model is proposed, using an Eshelby inclusion solution based homogenization method. Based on the numerical integration of the exact Green's function and using an appropriate coordinate frame rotation method, an efficient numerical algorithm is proposed to determine the Hill tensor for an arbitrarily oriented family of cracks embedded in a transversely isotropic elastic matrix. Based on this, the effective elastic properties of cracked materials are determined through a rigorous up-scaling procedure using three different homogenization schemes, and taking into account interactions between the initial material anisotropy and induced cracks. A specific damage criterion is then defined in the framework of irreversible thermodynamics to describe the progressive growth of damage. The proposed model is finally implemented in a computer code and applied to study mechanical responses of cracked materials in different loading paths. Again, effects of the initial anisotropy and homogenization schemes are investigated.