Reconstruction of random microstructures––a stochastic optimization problem

In the present paper the simulated annealing procedure is used to reconstruct plane and spatial dispersions of inclusions as observed on reference images of respective microstructures. The dispersion of centres of particles serves as reference distributions for reconstruction. The integral correlation function is used to define an objective function, which is identified as a sum of squared differences of nodal points of the integral correlation function for a reference and reconstructed dispersions. The reconstruction process is subject to various types of constraints. The geometrical constraint of topological entropy introduces a measure of arbitrariness of the polygonal or polyhedral tessellation associated with the point pattern of inclusion centres. Second geometrical constraint can be taken either as a pre-selected difference between a mean and standard deviation of distances of neighbouring inclusions or as a fulfilment of statistical t-tests and F-test for mean and standard deviation of distances, respectively. An attempt to implementation of constraints related to maximal stresses calculated at the inclusion interfaces has been also made and for plane dispersions effective results have been obtained. The results show, that reconstructed families of dispersions resemble the reference patterns with respect to selected criteria and, therefore, can be used for a further analysis to predict overall properties of underlying materials.