Damage as Gamma-limit of microfractures in anti-plane linearized   elasticity
  A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. In particular, damage is obtained as limit of periodically distributed microfractures. 
Lucia Scardia