A multiscale approach to damage configurational forces

A two-scale homogenization method is used to construct a damage model in the framework of configurational mechanics. The upscaling procedure allows for the identification of damage configurational forces as the result of the microscopic fracture analysis. The obtained damage equation incorporates stiffness degradation, material softening, unilaterality, induced anisotropy. The balance of configurational forces naturally captures a microscopic length, leading to size effects in the overall damage response. The new approach is illustrated in the case of brittle damage, for a three point bending test. Extended finite elements are used for the numerical modeling of macro-crack initiation and growth. The influence of the microscopic size on the failure initiation stress is analyzed and it is shown that this dependence follows a Hall-Petch type rule.