Quasi-unilateral conditions in anisotropic elasticity

A thermodynamic framework is proposed to model anisotropic elasticity different in tension and in compression. Based on Kelvin decomposition of the compliance tensor, it applies to any 3D loading. Coupling with damage is made considering fourth- and second-order damage tensors. The proposed formulation automatically satisfies the continuity of the stress tensor and of the energy release rate tensor. The particular case of initially isotropic materials is exposed.