Stochastic Continuum Damage Mechanics Using Spring Lattice Models

In this study, a planar spring lattice model is used to study the evolution of damage variable dL in disordered media. An elastoplastic softening damage constitutive law is implemented which introduces a cohesive length scale in addition to the disorder-induced one. The cohesive length scale affects the macroscopic response of the lattice with the limiting cases of perfectly brittle and perfectly plastic responses. The cohesive length scale is shown to affect the strength-size scaling such that the strength increases with increasing cohesive length scale for a given size. The formation and interaction of the microcracks is easily captured by the inherent discrete nature of the model and governs the evolution of dL . The proposed method provides a way to extract a mesoscale dependent damage evolution rule that is linked directly to the microstructural disorder.