Three-dimensional reconstruction of statistically optimal unit cells of polydisperse particulate composites from microtomography

Abstract

In this paper, we present a systematic approach for characterization and reconstruction of statistically optimal representative unit cells of polydisperse particulate composites. Microtomography is used to gather rich three-dimensional data of a packed glass bead system. First-, second-, and third-order probability functions are used to characterize the morphology of the material, and the parallel augmented simulated annealing algorithm is employed for reconstruction of the statistically equivalent medium. Both the fully resolved probability spectrum and the geometrically exact particle shapes are considered in this study, rendering the optimization problem multidimensional with a highly complex objective function. A ten-phase particulate composite composed of packed glass beads in a cylindrical specimen is investigated, and a unit cell is reconstructed on massively parallel computers. Further, rigorous error analysis of the statistical descriptors (probability functions) is presented and a detailed comparison between statistics of the voxel-derived pack and the representative cell is made.

Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

“…Others [46,54] have attempted an MC sampling strategy to compute probability functions, but on regular structured grids. An adaptive triangulation technique is used to overcome inefficiencies of structured grids.…”

“…Note that this pack was generated using a packing algorithm [43] based on the Lubachevsky-Stillinger method [44,45]. Others have computed one-, two-and three-point probability functions for systems of spheres for the purpose of quantifying the configuration [46,47]. However, computing these complex functions for the entire function domain, Ω, with the fidelity required by third-order statistical micromechanics models presented in §2b has not been previously accomplished.…”

Homogenization Methods and Multiscale Modeling: Nonlinear Problems

“…An example of this reconstruction procedure is presented here from Lee et al (2009), where particulate RUCs are reconstructed from a tomographically obtained data set for a granular system of polydisperse silica (see inset of Figure 5a). A large section (pack, see Figure 5b) from the tomographic data set (1445.37 × 1287.892 × 789.106 μm 3 ) containing 19 892 particles is analyzed.…”

“…Originating from the statistical mechanics community, the concept of a representative unit cell (RUC) is frequently used as well, rather than an RVE. The definition of an RUC essentially relies on statistical descriptors, and hence the morphology approximation error is better defined from a quantitative perspective (Povirk, 1995;Kumar et al, 2006Kumar et al, , 2008Lee et al, 2009 …”

Wang Tiles Local Tilings Created by Merging Edge-Compatible Finite Element Meshes

“…In this case the unit cell representing the original microstructure holds the same properties given by statistical descriptors as the source one [2]. Nevertheless, this approach uses only a single cell to describe the whole material and the stochastic heterogeneous material is transformed into unwanted periodic pattern of the same cells.…”