Computational Physics Group

Karel Matous









Reconstruction of Periodic Unit Cells of Multimodal

Random Particulate Composites

using Genetic Algorithms

N. Chennimalai Kumar2, K. Matous1,2 and P.H. Geubelle2

1Computational Science and Engineering
2Department of Aerospace Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.


We develop a procedure for characterization and reconstruction of periodic unit cells of highly filled, multi-modal, particulate composites. Rocpack, a particle packing software, is used to generate the solid propellant microstructures and one- and two-point probability functions are used to describe its statistical morphology. The reconstruction is carried out using a parallel Augmented Simulated Annealing algorithm with a novel mutation operator based on a mass-spring system to eliminate overlap and improve the code performance. Results from the reconstruction procedure, for four-phase random particulate composites of 40%-70% packing fraction, are detailed to demonstrate the capabilities of the reconstruction model. The presented results suggest good convergence and repeatability of the optimization scheme, even for high volume fractions, and good scalability of the algorithm.


An effective method has been presented to characterize and reconstruct the complex microstructure of a random highly packed, multi-modal, particulate composite by a simplified periodic unit cell that is statistically (geometrically) similar to the original microstructure. It is important to note that the reconstructed periodic unit cells are only representative from a geometrical statistics point of view and that the representativity of the PUC must also account for the physical processes of interest (Swaminathan and Ghosh [23]). However, the construction of a geometrically equivalent periodic unit cell is an important first step in describing behavior of complex particulate materials, such as solid propellants. In this work, the micrographs have been computationally generated using a packing software called Rocpack, which has been tested and compared to available experimental data. For the present study, one- and two-point probability functions have been identified as the suitable statistical descriptors and the assumptions of ergodicity, homogeneity and statistical isotropy have been numerically assessed.

A stochastic optimization method called Augmented Simulated Annealing has been used to optimize the positions of particles inside the periodic cell, such that probability functions are similar to those from the original pack. The optimization scheme has been implemented in parallel allowing for the study of large data sets with large particle size variations and high packing content. A new mutation operator, based on a mass-spring system, has been developed to eliminate the particle overlap and to speed up the computations.

Reconstruction of periodic unit cells has been performed on four-phase random particulate composite packs of 40-70% packing fractions. The reconstruction results show good convergence and repeatability of the genetic algorithm and the statistics of the reconstructed cells compare well with those of the original


The authors would like to gratefully acknowledge the support from ATK/Thiokol (ATK-21316), with J. Thompson and Dr. I. L. Davis serving as program monitors, and from the Center for Simulation of Advanced Rockets (CSAR) under contract number B523819 by the U.S. Department of Energy as a part of its Advanced Simulation and Computing (ASC) program. We would also like to thank Dr. T.L. Jackson and his team for providing Rocpack & for helpful discussions.

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2009 Notre Dame and Dr. Karel Matous