An optimum approximation of n-point correlation functions of random heterogeneous material systems

M. Baniassadi, M. Safdari, H. Garmestani, Said Ahzi, P. H. Geubelle, Y. Remond

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

An approximate solution for n-point correlation functions is developed in this study. In the approximate solution, weight functions are used to connect subsets of (n-1)-point correlation functions to estimate the full set of n-point correlation functions. In previous related studies, simple weight functions were introduced for the approximation of three and four-point correlation functions. In this work, the general framework of the weight functions is extended and derived to achieve optimum accuracy for approximate n-point correlation functions. Such approximation can be utilized to construct global n-point correlation functions for a system when there exist limited information about these functions in a subset of space. To verify its accuracy, the new formulation is used to approximate numerically three-point correlation functions from the set of two-point functions directly evaluated from a virtually generated isotropic heterogeneous microstructure representing a particulate composite system. Similarly, three-point functions are approximated for an anisotropic glass fiber/epoxy composite system and compared to their corresponding reference values calculated from an experimental dataset acquired by computational tomography. Results from both virtual and experimental studies confirm the accuracy of the new approximation. The new formulation can be utilized to attain a more accurate approximation to global n-point correlation functions for heterogeneous material systems with a hierarchy of length scales.

Original languageEnglish
Article number074905
JournalJournal of Chemical Physics
Volume140
Issue number7
DOIs
Publication statusPublished - 21 Feb 2014
Externally publishedYes

Fingerprint

approximation
set theory
formulations
composite materials
Set theory
glass fibers
Large scale systems
particulates
hierarchies
tomography
microstructure
estimates
Tomography
Microstructure

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

An optimum approximation of n-point correlation functions of random heterogeneous material systems. / Baniassadi, M.; Safdari, M.; Garmestani, H.; Ahzi, Said; Geubelle, P. H.; Remond, Y.

In: Journal of Chemical Physics, Vol. 140, No. 7, 074905, 21.02.2014.

Research output: Contribution to journalArticle

Baniassadi, M. ; Safdari, M. ; Garmestani, H. ; Ahzi, Said ; Geubelle, P. H. ; Remond, Y. / An optimum approximation of n-point correlation functions of random heterogeneous material systems. In: Journal of Chemical Physics. 2014 ; Vol. 140, No. 7.
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