Multi Scale Random Models of Complex Microstructures

Abstract

Many nanocomposite materials are obtained by dispersing a charge in a matrix. Due to the conditions of mixing, the arrangement of the charge usually presents some heterogeneity at different scales. In order to predict the effective properties of such composites (like the dielectric permittivity or the elastic moduli), it is necessary to know the properties of the two components (charge and matrix), and their spatial distribution. To fulfil this project, we developed a general methodology in several steps: the morphology is summarized by multi-scale random models accounting for the heterogeneous distribution of aggregates. The identification of models is made from image analysis. It is then used for the prediction of effective properties by estimation, or by numerical simulations. Our approach is illustrated by various examples of multi-scale models: Boolean random sets based on Cox point processes and various random grains (spheres, cylinders), showing a very low percolation threshold and therefore a high conductivity or elastic moduli for a low charge content; multi-scale iterations of random media.