Friction-Damage coupled models for brittle materials

By considering a tensorial description of the damage and of the unilateral and frictional effects on the displacement jump across the crack faces, an anisotropic constitutive model based on the assumption of linear elastic matrix weakened by microcraks is derived. Damage and sliding evolutions are obtained on the basis of proper limit conditions and associated flow rules. This treatment implies a different tensile-compressive response because under triaxial tensile stress states only the damage limit condition is effective, otherwise this condition must be coupled with the frictional sliding one. By considering proportional loading paths, limit strength domains can be obtained which are depending on the microcracking parameters and on the friction coefficient. Finally, the influence of the internal friction on the limit strength domains provided by the presented model is shown with reference to biaxial stress states