Toughening by crack deflection in the homogenization of brittle   composites with soft inclusions
  We present a simple example of toughening mechanism in the homogenization of composites with soft inclusions, produced by crack deflection at microscopic level. We show that the mechanism is connected to the irreversibility of the crack process. Because of that it cannot be detected through the standard homogenization tool of the $\Gamma$-convergence. 
Marco Barchiesi
math.AP