Multi Scale Random Sets: From Morphology to Effective Behaviour

Abstract

Complex microstructures in materials and in biology often involve multi-scale heterogeneous textures, that we model by random sets derived from Mathematical Morphology. Our approach starts from 2D or 3D images; a complete morphological characterization is performed, and used for the identification of a model of random structure. Simulations of realistic microstructures are introduced in a numerical solver to compute appropriate fields (electric, elastic, velocity, ...) and to estimate the effective properties by numerical homogenization, accounting for scale dependent statistical fluctuations of the fields.