A new approximation for the three-point probability function

A. Mikdam, A. Makradi, Said Ahzi, H. Garmestani, D. S. Li, Remond Y. Remond

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

Statistical continuum theory based approaches are commonly used for the computation of the effective properties of heterogeneous materials. Statistical distribution and morphology of the microstructure are represented by n-point probability function. One-point probability function statistical representation of the microstructure leads to volume fraction dependent homogenization. However, second and higher order probability functions include the information of phase distribution and morphology. Most statistical based homogenization methods are limited to two-point probability function due to the lack of simple approximation of higher order probability functions that can be easily exploited. In this paper, a new approximation of the three-point probability function is proposed and discussed. The new approximation results are compared to existing approximations from the literature and to the real probability functions calculated from a computer generated two-phase micrographs.

Original languageEnglish
Pages (from-to)3782-3787
Number of pages6
JournalInternational Journal of Solids and Structures
Volume46
Issue number21
DOIs
Publication statusPublished - 15 Oct 2009
Externally publishedYes

Fingerprint

Probability function
Approximation
approximation
homogenizing
Microstructure
Higher Order
Homogenization method
Homogenization Method
Heterogeneous Materials
microstructure
Effective Properties
Statistical Distribution
statistical distributions
Volume Fraction
Homogenization
Volume fraction
Continuum
continuums
Dependent

Keywords

  • Heterogeneous media
  • Probability functions
  • Statistical continuum

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)
  • Condensed Matter Physics
  • Applied Mathematics
  • Modelling and Simulation

Cite this

A new approximation for the three-point probability function. / Mikdam, A.; Makradi, A.; Ahzi, Said; Garmestani, H.; Li, D. S.; Y. Remond, Remond.

In: International Journal of Solids and Structures, Vol. 46, No. 21, 15.10.2009, p. 3782-3787.

Research output: Contribution to journalArticle

Mikdam, A. ; Makradi, A. ; Ahzi, Said ; Garmestani, H. ; Li, D. S. ; Y. Remond, Remond. / A new approximation for the three-point probability function. In: International Journal of Solids and Structures. 2009 ; Vol. 46, No. 21. pp. 3782-3787.
@article{7aef9d79f5a64b638cfe9dda1fa61cbb,
title = "A new approximation for the three-point probability function",
abstract = "Statistical continuum theory based approaches are commonly used for the computation of the effective properties of heterogeneous materials. Statistical distribution and morphology of the microstructure are represented by n-point probability function. One-point probability function statistical representation of the microstructure leads to volume fraction dependent homogenization. However, second and higher order probability functions include the information of phase distribution and morphology. Most statistical based homogenization methods are limited to two-point probability function due to the lack of simple approximation of higher order probability functions that can be easily exploited. In this paper, a new approximation of the three-point probability function is proposed and discussed. The new approximation results are compared to existing approximations from the literature and to the real probability functions calculated from a computer generated two-phase micrographs.",
keywords = "Heterogeneous media, Probability functions, Statistical continuum",
author = "A. Mikdam and A. Makradi and Said Ahzi and H. Garmestani and Li, {D. S.} and {Y. Remond}, Remond",
year = "2009",
month = "10",
day = "15",
doi = "10.1016/j.ijsolstr.2009.07.004",
language = "English",
volume = "46",
pages = "3782--3787",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",
number = "21",

}

TY - JOUR

T1 - A new approximation for the three-point probability function

AU - Mikdam, A.

AU - Makradi, A.

AU - Ahzi, Said

AU - Garmestani, H.

AU - Li, D. S.

AU - Y. Remond, Remond

PY - 2009/10/15

Y1 - 2009/10/15

N2 - Statistical continuum theory based approaches are commonly used for the computation of the effective properties of heterogeneous materials. Statistical distribution and morphology of the microstructure are represented by n-point probability function. One-point probability function statistical representation of the microstructure leads to volume fraction dependent homogenization. However, second and higher order probability functions include the information of phase distribution and morphology. Most statistical based homogenization methods are limited to two-point probability function due to the lack of simple approximation of higher order probability functions that can be easily exploited. In this paper, a new approximation of the three-point probability function is proposed and discussed. The new approximation results are compared to existing approximations from the literature and to the real probability functions calculated from a computer generated two-phase micrographs.

AB - Statistical continuum theory based approaches are commonly used for the computation of the effective properties of heterogeneous materials. Statistical distribution and morphology of the microstructure are represented by n-point probability function. One-point probability function statistical representation of the microstructure leads to volume fraction dependent homogenization. However, second and higher order probability functions include the information of phase distribution and morphology. Most statistical based homogenization methods are limited to two-point probability function due to the lack of simple approximation of higher order probability functions that can be easily exploited. In this paper, a new approximation of the three-point probability function is proposed and discussed. The new approximation results are compared to existing approximations from the literature and to the real probability functions calculated from a computer generated two-phase micrographs.

KW - Heterogeneous media

KW - Probability functions

KW - Statistical continuum

UR - http://www.scopus.com/inward/record.url?scp=69249216511&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69249216511&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2009.07.004

DO - 10.1016/j.ijsolstr.2009.07.004

M3 - Article

VL - 46

SP - 3782

EP - 3787

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 21

ER -