Morphological complexity of material microstructures: From stochastic models to fracture estimation

In this paper the basic methodology (the underlying ideas, formulations and some recent results) for modelling and analysis of random material microstructures is reviewed. In particular, the Poisson-type models of dispersed-type random microstructures and the tessellation patterns for random polyhedral/grain materials are examined.In the second part of the paper (Sections 4–5) the random microstructural stresses and their effect on the stress intensity and on the crack path are discussed and illustrated numerically.