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Research Papers

Stochastic Morphological Modeling of Random Multiphase Materials

[+] Author and Article Information
Lori Graham-Brady

Department of Civil Engineering, Johns Hopkins University, 3400 North Charles Street, Latrobe Hall, Baltimore, MD 21218

X. Frank Xu

Department of Civil, Environmental, and Ocean Engineering, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ 07030

J. Appl. Mech 75(6), 061001 (Aug 15, 2008) (10 pages) doi:10.1115/1.2957598 History: Received September 28, 2005; Revised January 09, 2007; Published August 15, 2008

A short-range-correlation (SRC) model is introduced in the framework of Markov/Gibbs random field theory to characterize and simulate random media. The Metropolis spin-flip algorithm is applied to build a robust simulator for multiphase random materials. Through development of the SRC model, several crucial conceptual ambiguities are clarified, and higher-order statistical simulation of random materials becomes computationally feasible. In the numerical examples, second- and third-order statistical simulations are demonstrated for biphase random materials, which shed light on the relationship between nth-order correlation functions and morphological features. Based on the observations, further conjectures are made concerning some fundamental morphological questions, particularly for future investigation of physical behavior of random media. It is expected that the SRC model can also be extended to third- and higher-order simulations of non-Gaussian stochastic processes such as wind pressure, ocean waves, and earthquake accelerations, which is an important research direction for high fidelity simulation of physical processes.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Half window used in the calculation of energy (Eqs. 15,16) in SRC formulation

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Figure 2

Specific morphologies studied in this work

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Figure 3

The second-order SRC model for P2 with different SRC window sizes (α1=0.7, α2=1.0), with the respective volume fraction for each sample

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Figure 4

Sample (target) covariance of P2: (left) profile; (right) contour

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Figure 5

Second-order simulation for P5 with different SRC window sizes (α1=0.3, α2=1.0)

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Figure 6

Third-order simulation for P4 with different SRC window sizes

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Figure 7

Third-order simulation for P5 with different SRC window sizes

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Figure 8

Samples generated based on Patterns P1–P6, using the second-order SRC model (α1=0.7, α2=1.0, α3=0), the third-order SRC model (α1=α2=0, α3=1.0), and the denoised third order SRC model

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Figure 9

Evolution of energy (error) in sample generation of P5: (a) second-order SRC model; (b) third-order SRC model

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