Reconstruction of random material microstructures: patterns of maximum entropy

This work is focused on the reconstruction of the probability distributions for the basic (topological and metric) characteristics of polycrystalline, random space-filling aggregates of grains (cells). The method is inspired by the Gibbsian ensemble method known in classical statistical physics/mechanics. Among all possible distributions of the microstructural parameters we are looking for the distributions which are compatible with the constraints representing the available macro or mezoscopic information. Specifically, we show how the idea of Gibbs ensembles can be used for random polyhedral space-filling models, such as random tessellation. The microstructural configurations are characterized by a number of parameters and their mutual relations in the aggregate (the consistency requirements). These parameters define a microstate of the system considered. We characterize the unknown probabilities of the microstates making use of the ‘macro’—information given by the appropriate average values defined on microstates, and then—using the method of maximum information entropy. In particular, some specific microstructures are treated numerically and illustrated graphically.