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.
Abstract
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.
Conclusions
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
packs.
Acknowledgment
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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© 2007 UIUC and Dr. Karel
Matous