On optimization techniques to reconstruct microstructures of random heterogeneous media

In recent years, a tremendous increase in the applications of composite materials has been observed. The variability in their composition dramatically affects their overall properties, resulting in materials with lower weight, increased stiffness and higher strength. The study of the material behaviour in non-trivial cases can be carried out adopting numerical tools that require realizations of the microstructures of the random heterogeneous media (RHM). The reconstruction of the microstructure of (RHM) can be seen as an optimization problem where a set of target correlation functions are prescribed, based on limited microstructural information. The reconstruction methods proceed to find realizations that best match the target correlation functions. As a result, many different optimization procedures have been recently developed to address the problem of the generation of realizations of random media. In this work, an optimization technique based on the genetic algorithm (GA) is proposed to reconstruct the microstructure of the RHM based on minimal microstructure information. The proposed approach is compared with the simulated annealing (SA) technique and with the maximum entropy (MaxEnt) method. A number of numerical examples are performed to quantify the performance of these reconstruction techniques in terms of accuracy of the solution, stability of the method and computational efforts. Finally, an efficient hybrid approach to reconstruct samples of the microstructure of RHM that combines the robustness and the good performances of the GA with the accuracy of the SA is suggested.