title: An optimum approximation of n-point correlation functions of random heterogeneous material systems.
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.
authors.affiliation: School of Mechanical Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran.
authors.forename: M
authors.initials: M
authors.lastname: Baniassadi
authors.affiliation: Aerospace Engineering Department, University of Illinois, 104 S Wright St., Urbana, Illinois 61801, USA.
authors.forename: M
authors.initials: M
authors.lastname: Safdari
authors.affiliation: School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Drive N.W., Atlanta, Georgia 30332-0245, USA.
authors.forename: H
authors.initials: H
authors.lastname: Garmestani
authors.affiliation: University of Strasbourg, ICube/CNRS, 2 Rue Boussingault, 67000 Strasbourg, France.
authors.forename: S
authors.initials: S
authors.lastname: Ahzi
authors.affiliation: Aerospace Engineering Department, University of Illinois, 104 S Wright St., Urbana, Illinois 61801, USA.
authors.forename: P H
authors.initials: PH
authors.lastname: Geubelle
authors.affiliation: University of Strasbourg, ICube/CNRS, 2 Rue Boussingault, 67000 Strasbourg, France.
authors.forename: Y
authors.initials: Y
authors.lastname: Remond