An isotropic unilateral damage model coupled with frictional sliding for quasi-brittle materials

• A new damage model for quasi-brittle materials is proposed.
• Both unilateral behaviors and inelastic strains have been taken into account.
• A particular attention is paid to the continuous differentiability of thermodynamic potential.
• The model ensures the continuity of the inelastic stress–strain response.

In this paper, we present an original extension of an isotropic damage model for quasi-brittle materials and assess its predictive capabilities. The proposed model accounts not only for unilateral behavior related to the opening and closure of microcracks but also for inelastic strains reflecting the frictional sliding along closed microcracks. More importantly, owing to its careful mathematical formulation with a particular attention paid to the continuous differentiability of the underlined thermodynamic potential, the model ensures the continuity of the inelastic stress–strain response. First applications show that it is able to predict the asymmetric behavior and hysteretic response of microcracked materials such as concrete and some rocks