Internal Variable Representation of Microcrack Induced Inelasticity in Brittle Materials

For brittle materials strained in compression, nonlinear constitutive equations are developed within the thermodynamic framework with microstructural internal variables. The sliding crack dissipative micromechanism, activated on preexisting dilutely distributed flaws, is assumed to govern the macroscopic deformation. The losses of energy resulting from frictional sliding on closed preexisting flaws, wing crack propagation, and wing crack rotation are included in the analysis. Two models (displacement-driven vs traction-driven) of the basic deformational micromechanism are considered in detail. The obtained incremental stress-strain relations are compared with the corresponding kinematic solutions available in the literature.