A combined fracture‐micromechanics model for tensile strain‐softening in brittle materials, based on propagation of interacting microcracks

Strain‐softening is the decline in stress at increasing strain. Although microcracking is a commonly accepted reason for strain‐softening, the majority of theoretical developments involve macroscopic damage evolution laws. To improve this situation, we propose a micromechanics‐based damage evolution law by combining (i) the propagation criterion for a single penny‐shaped crack embedded in an infinite matrix subjected to remote stresses (taken from linear‐elastic fracture mechanics) and (ii) stiffness estimates for representative material volumes comprising interacting microcracks (taken from continuum micromechanics). This combination allows for modelling 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 behaviour under strain control: (i) continuous strain‐softening, which occurs in case of initial damage above 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.