A refined micromechanical damage–friction model with strength prediction for rock-like materials under compression

Inelastic deformation and damage evolution at microdefects are two essential nonlinear mechanisms that govern macroscopic mechanical behaviors of quasi-brittle solids. The present paper deals in a unified framework with two dissipative processes in microcracks: inelastic deformation due to frictional sliding and damage by crack growth, usually arising and strongly coupled in cohesive materials under compression. Contributions by this work are threefold: (i) based on the Mori–Tanaka method, the free enthalpy of the representative elementary volume composed of a matrix phase and randomly oriented and distributed penny-shaped microcracks is determined for the general case of multiple crack families. The constitutive formulations are now presented in an elegant manner by using two orientation-dependent tensorial operators; (ii) the friction criterion is formulated in terms of the local stress applied onto microcracks. This local stress contains a back stress term that allows unified modeling of material hardening/softening behavior: friction-induced hardening is attributed to the cumulation of frictional shearing while damage-related softening is induced by crack growth and coalescence; (iii) originally, strength prediction is achieved through damage–friction coupling analyses. In that process, a basic feature of the damage resistance is revealed, leading to a novel damage criterion suitable for describing and modeling nonlinear mechanical behavior of quasi-brittle materials. Moreover, trans-scale relationship between the parameters in the local criteria and experimental data from laboratory tests is set up, which is always appealing in multiscale modeling. As a first phase of validation, the refined micromechanical model is finally applied to simulate laboratory tests on a granite under triaxial compression.