Damage-cluster distributions and size effect on strength in compressive failure.

We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive-damage model. The model explicitly accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage clusters, as well as the evolution of an order parameter--the size of the largest damage cluster--argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments.