### 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 language | English |
---|---|

Article number | 074905 |

Journal | Journal of Chemical Physics |

Volume | 140 |

Issue number | 7 |

DOIs | |

Publication status | Published - 21 Feb 2014 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Chemical Physics*,

*140*(7), [074905]. https://doi.org/10.1063/1.4865966

**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.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 140, no. 7, 074905. https://doi.org/10.1063/1.4865966

}

TY - JOUR

T1 - An optimum approximation of n-point correlation functions of random heterogeneous material systems

AU - Baniassadi, M.

AU - Safdari, M.

AU - Garmestani, H.

AU - Ahzi, Said

AU - Geubelle, P. H.

AU - Remond, Y.

PY - 2014/2/21

Y1 - 2014/2/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84898829658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898829658&partnerID=8YFLogxK

U2 - 10.1063/1.4865966

DO - 10.1063/1.4865966

M3 - Article

VL - 140

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

M1 - 074905

ER -