A damage model with non-convex free energy for quasi-brittle materials

A state coupling between the hydrostatic (volumetric) and deviatoric parts of the free energy is introduced in a damage mechanics model relevant for the quasi-brittle materials. It is shown that it describes the large dilatancy of concrete under compression and the different localization angles and damage levels in tension and compression. A simple isotropic description is used, although similar ideas can be extended to anisotropic damage. The model is identified with respect to tensile and compression tests and validated on bi-compression and bi-tension. Fully written in three dimensions under the framework of thermodynamics of irreversible processes, it allows further developments within a finite element code.