A Model of Anisotropic Damage by Mesocrack Growth; Unilateral Effect

A three-dimensional model of anisotropic damage by mesocrack growth is first described in its basic version, employing a second-order tensorial damage variable. The model—concerning rate-independent, small strain, isothermal behaviour—allows to take into account residual effects due to damage and reduces any system of mesocracks to three equivalent orthogonal sets. This first version is then extended to account for elastic moduli recovery due to crack closure. Micromechanical considerations impose to employ a fourth-order crack-related tensor when the mesocracks are constrained against opening. Unlike some models which do not avoid (or rectify a posteriori) discontinuities of the stress-strain response, the approach herein ensures a priori the stress continuity and allows to express a convenient macroscopic opening-closure criterion. Nevertheless, the new formulation maintains the orthotropy of the effective properties (instead of an eventual, more general form of anisotropy). Finally, it appears that the extended version does not introduce additional material constants compared to the basic version. The model is tested by simulating the behaviour of Fontainebleau sandstone.