Micromechanics of anisotropic brittle damage : comparative analysis between a stress based and a strain based formulation
Résumé
Brittle anisotropic damage with unilateral effects due to microcracking phenomena is investigated here within a three-dimensional micromechanical approach. Emphasis is put on comparison between a stress-based and a strain-based approaches. For microcracked media, we establish general expressions of the macroscopic energy potentials which incorporate the relevant microstructural quantities (mesocracks density parameter and orientation, mesocracks displacements jump). Assuming then that damage by mesocracks growth is the main dissipative mechanism of the considered materials, we derive the damage-dependent thermodynamics potentials accounting for mesocracks closure. The mesocracks closure criterion as well as the elastic moduli recovery conditions are carefully addressed. Then, a suitable damage potential based on the use of the damage-energy release rate is proposed and comparatively illustrated in various stress subspaces. The local integration of the rate form of the two constitutive model is done using an elastic predictordamage corrector scheme. Finally, it is shown, on the basis of some numerical simulations, that these formulations are consistent with experimental data obtained on a sandstone. However, at high stress (damage) levels, significant differences are noted between the two formulations, especially for pronounced evolving microstructure and strong damage-induced anisotropy.