Research Papers

Stochastic Reassembly Strategy for Managing Information Complexity in Heterogeneous Materials Analysis and Design

[+] Author and Article Information
Hongyi Xu, Hua Deng

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

M. Steven Greene

Theoretical & Applied Mechanics,
Northwestern University,
Evanston, IL 60208

Dmitriy Dikin

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208;
Department of Physics and Astronomy,
Northwestern University,
Evanston, IL 60208

Catherine Brinson

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208;
Department of Material Science and Engineering,
Northwestern University,
Evanston, IL 60208

Wing Kam Liu

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

George Papakonstantopoulos

Global Materials Science Division,
The Goodyear Tire & Rubber Company,
Akron, OH 44305

Mike Poldneff

External Science & Technology Division,
The Goodyear Tire & Rubber Company,
Akron, OH 44309

Wei Chen

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: weichen@northwestern.edu

A heterogeneous material, by definition, contains multiple phases. For instance, filled elastomers contain polymer-like synthetic rubber and filler-like silica, nanoclay, or carbon black. These constituents have individual properties. However, designers using the composite material are interested in how the multiple phases behave together (for instance the tensile strength). The properties of the whole material system are labeled “apparent” and are often quite different than the sum of the constituents' properties.

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 22, 2012; final manuscript received June 19, 2013; published online September 11, 2013. Assoc. Editor: Michael Kokkolaras.

J. Mech. Des 135(10), 101010 (Sep 11, 2013) (12 pages) Paper No: MD-12-1427; doi: 10.1115/1.4025117 History: Received August 22, 2012; Revised June 19, 2013

Design of high performance materials system requires highly efficient methods for assessing microstructure–property relations of heterogeneous materials. Toward this end, a domain decomposition, affordable analysis, and subsequent stochastic reassembly approach is proposed in this paper. The approach hierarchically decomposes the statistically representative cell (representative volume element (RVE)) into computationally tractable unrepresentative ones (statistical volume element (SVE)) at the cost of introducing uncertainty into subdomain property predictions. Random property predictions at the subscale are modeled with a random field that is subsequently reassembled into a coarse representation of the RVE. The infinite dimension of microstructure is reduced by clustering SVEs into bins defined by common microstructure attributes, with each bin containing a different apparent property random field. We additionally mitigate the computational burden in this strategy by presenting an algorithm that minimizes the number of SVEs required for convergent random field characterization. In the proposed method, the RVE thus becomes a coarse representation, or mosaic, of itself. The mosaic approach maintains sufficient microstructure detail to accurately predict the macroproperty but becomes far cheaper from a computational standpoint. A nice feature of the approach is that the stochastic reassembly process naturally creates an apparent-SVE property database whose elements may be used as mosaic building blocks. This feature enables material design because SVE-apparent properties become the building blocks of new, albeit conceptual, material mosaics. Some simple examples of possible designs are shown. The approach is demonstrated on polymer nanocomposites.

Copyright © 2013 by ASME
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Grahic Jump Location
Fig. 1

The concept of upscaling properties in multiscale methods with RVE and SVE. RVEs produce deterministic apparent material properties; SVEs introduce uncertainty. When comparing the RVE (top) to the SVE (bottom), the material is the same. The difference is only the window size lSVE<lRVE.

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Fig. 2

Comparison of proposed strategy and the typical homogenization approach. The method alters the representation of the RVE to a coarse version of itself through the hierarchical decomposition and reassembly processes. SVEs with similar morphology features are classified into different clusters marked by different color in the coarsened RVE.

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Fig. 3

Material property upscaling from SVE to RVE level using mosaic image of SVE clusters

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Fig. 4

Illustration of “elbow point” in optimal cluster number determination

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Fig. 5

The flowchart of the sample size determination process

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Fig. 6

Property for pure polymer (G′ and G″). G′ measures the stored energy, representing the elastic portion, and G″ measures the energy dissipated as heat, representing the viscous portion.

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Fig. 7

(a) Double layer gradient interphase model in FEM; (b) viscoelastic properties of interphase

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Fig. 8

Two examples of comparisons between SVE clusters generated by clustering method based solely on gray level values (a, b) and clustering method based on five key microstructure descriptors (c, d)

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Fig. 9

Comparison of standard deviations of middle points' value on the G′ and G″ curves in each cluster. The standard deviations are sorted following the ascending trend instead of following the sequence of cluster number to facilitate visual comparison.

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Fig. 10

The reduced sample sets' sizes compared with full sample sets' sizes of each cluster

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Fig. 11

The distributions of values at five frequencies on the tan δ curve are compared with determine the sample size

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Fig. 12

Comparison of RVE material damping property (G′ and G″). Meanings of titles in the legend: (1) DNS, direct numerical simulation; (2) real SVE properties: using properties of real SVE images divided for RVE image; (3) regenerated SVE properties, all SVE samples: regenerated SVE properties using random field model established by all SVE sample images; (4) regenerated SVE properties, α = X: regenerated SVE properties using random field model based on minimized sample set. X = 0.5 is used in t test.

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Fig. 13

Simulation accuracy and computation time cost of reassembly approach using different SVE sizes

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Fig. 14

Microstructure descriptors and correlation functions for two material designs

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Fig. 15

Reconstructed microstructures, mosaic RVE, and the correspondent properties




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