A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction effects

This paper is devoted to micromechanical modeling of isotropic damage in brittle materials. The damaged materials will be considered as heterogeneous media composed of solid matrix weakened by isotropically distributed microcracks. The original contribution of the present work is to provide a proper micromechanical thermodynamic formulation for damage-friction modeling in brittle materials with the help of Eshelby’s solution to matrix-inclusion problems. The elastic and plastic strain energy involving unilateral effects will be fully determined. The condition of microcrack opening–closure transition will be determined in both strain-based and stress-based forms. The effect of spatial distribution of microcracks will also be taken into account. Further, the damage evolution law is formulated in a sound thermodynamic framework and inherently coupled with frictional sliding. As a first phase of validation, the proposed micromechanical model is finally applied to reproduce basic mechanical responses of ordinary concrete in compression tests.