A time-dependent damage law in solids: a homogenization approach

The theoretical developments and the numerical applications of a time-dependent damage law is presented. This law is deduced from considerations at the micro-scale where non-planar growth of micro-cracks, following a subcritical propagation criterion, is assumed. The passage from micro-scale to macro-scale is done through an asymptotic homogenization approach. The model is built in two steps. First, the effective coefficients are calculated at the micro-scale in finite periodical cells, with respect to the micro-cracks length and their orientation. Then, a subcritical damage law is developed in order to establish the evolution of damage. As shown by numerical simulations, the developed model enables to reproduce the long-term behavior encountering relaxation and creep effects.