Propagation of interacting microcracks results in macroscopic tensile strain-softening of brittle materials - A combined fracture and micromechanics approach

We propose a micromechanics-based damage evolution law by combining the propagation criterion for a single penny-shaped crack embedded in an infinite matrix subjected to remote stresses (taken from linear-elastic fracture mechanics) with stiffness estimates for representative material volumes comprising interacting microcracks (taken from continuum micromechanics). This allows for modeling tensile strain-softening as a result of propagation of interacting microcracks, i.e. as a microstructural effect. The initial degree of damage, i.e. the initial microcrack size and the number of microcracks per unit volume, implies two different types of model-predicted tensile strain-softening behavior under strain control: (i) continuous strain-softening, which occurs in case of initial damage beyond a critical value, and (ii) an instantaneous stress drop at the peak load ("snap-back"), which occurs in case of initial damage below a critical value.