## Reconstruction of Periodic Unit Cells of Multimodal

## Random Particulate Composites

## using Genetic Algorithms

N. Chennimalai Kumar^{2}, K. Matous^{1,2}
and P.H. Geubelle^{2}

^{1}Computational Science and Engineering

^{2}Department 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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