Microcracks closure effects in initially orthotropic materials

Microcracking is one of the basic mechanisms of inelastic deformation for a large class of anisotropic materials such as brittle matrix composites. Even at fixed microcracks density, the macroscopic behavior of these materials is very complex due to the combination of two specific features of such deteriorating phenomenon. First, the oriented nature of microcracks induces an evolution of the material symmetry (interaction between the initial anisotropy and the microcracks induced one). Secondly, a change in the elastic response of the material is expected, based on whether microcracks are open or closed in response to specific loading situations (the so-called “unilateral effect”). The present paper is devoted to a continuum micromechanics-based investigation of the resulting – generally fully – anisotropic multilinear response of orthotropic materials containing microcracks. The procedure leads to the proposal of a closed-form expression of the macroscopic free energy corresponding to 2D initially orthotropic materials weakened by arbitrarily oriented microcracks systems. The established results provide a complete quantification of both coupling effects of anisotropies and elastic moduli recovery phenomena induced by microcracks closure. A particular emphasis is put on the importance of Hill lemma for the derivation of these results which constitute a basis to the micro-macro modeling of damage process in initially orthotropic media.