An anisotropic model of damage and frictional sliding for brittle materials

The paper provides important developments for the model of anisotropic damage by mesocrack growth, accounting for unilateral behaviour relative to crack closure (Dragon and Halm, 1996, Halm and Dragon, 1996). Frictional sliding of closed microcrack systems is introduced here as an additional dissipative mechanism, which is considered to be coupled with the primary dissipative mechanism (damage by microcrack growth). Indeed, accounting for frictional sliding completes the description of moduli recovery in the existing model by adding to the normal moduli recovery effect (normal with respect to the crack plane) the substantial recovery of shear moduli. In parallel to damage modelling, the internal variable related to frictional sliding is a second-order tensor. Even if the unilateral effect and friction incipience are characterized by a discontinuity of effective moduli, it is crucial to ensure continuity of the energy and stress-response. Relevant conditions are proposed to ensure this. As far as frictional sliding is concerned, and unlike most of the models based on the classical Coulomb law, the corresponding criterion is given here in the space of thermodynamic forces representing a form of energy release with respect to the sliding internal variable. It appears that the normality rule in the latter space for sliding evolution is not physically contradictory with the observed phenomenon. The pertinence of the proposed theory, relative to the maximum dissipation hypothesis for both mechanisms, is illustrated by simulating loading paths involving damage and friction effects.