Three-Dimensional Reconstruction of Statistically Optimal Unit Cells
of Multimodal Particulate Composites

B.C. Collins

Computational Science and Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801 USA

K. Matouš

Aerospace and Mechanical Engineering Department
University of Notre Dame
Notre Dame, IN 46556, USA

D. Rypl

Department of Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic


In the current digital age, it is befitting that complex heterogeneous materials, such as solid propellants, are characterized by digital computational and/or experimental techniques. Of those, microcomputer tomography (micro-CT) and advanced packing algorithms are the most popular for identifying the statistics of multimodal, random, particulate composites. In this work, we develop a procedure for the characterization and reconstruction of periodic unit cells of highly filled, multimodal, particulate composites from a packing algorithm. Rocpack, a particle packing software, is used to generate the solid propellant microstructures, and one-, two-, and three-point probability functions are used to describe their statistical morphology. However, both the experimentally scanned or computationally designed packs are usually nonoptimal in size and likely too big to be fully numerically resolved when complex nonlinear processes, such as combustion, decohesion, matrix tearing, etc., are modeled. Thus, domain reduction techniques, which can reconstruct the optimal periodic unit cell, are important to narrow the problem size while preserving the statistics. The three-dimensional reconstruction is carried out using a parallel augmented simulated annealing algorithm. Then, the resulting cell geometries are discretized, taking into consideration the periodic layout using our master/slave approach implemented into a sophisticated meshing generator T3D. Final discretized geometries show only a small loss of volume fraction. Particulate systems composed of 40 and 70% volume fractions are investigated, and the unit cells are reconstructed such that the statistical correspondence to the original packs is maintained.