Periodization of random media and representative volume element size for linear composites

Karam Sab; Boumediene Nedjar

doi:10.1016/j.crme.2004.10.003

Periodization of random media and representative volume element size for linear composites

Presented by: Pierre Suquet

Karam Sab ¹ ; Boumediene Nedjar ¹

¹ Institut Navier, LAMI, École nationale des ponts et chaussées, 6-8, avenue Blaise Pascal, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2, France

Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 187-195.

Abstract
Résumé

Several existing numerical studies show that the effective linear properties of random composites can be accurately estimated using small volumes subjected to periodic boundary conditions – more suitable than homogeneous strain or stress boundary conditions – providing that a sufficient number of realizations are considered. Introducing the concept of periodization of random media, this Note gives a new definition of representative volume element which leads to estimates of its minimum size in agreement with existing theoretical results. A qualitative convergence criterion for the numerical simulations is proposed and illustrated with finite element computations.

Plusieurs simulations numériques montrent que les propriétés effectives linéaires des matériaux aléatoires peuvent être calculées sur de petits échantillons soumis à des conditions limites périodiques – plus adaptées que les conditions uniformes en contrainte ou en déformation – pourvu que le nombre d'échantillons considérés soit suffisamment grand. En introduisant le concept de périodisation des milieux aléatoires, cette Note donne une nouvelle définition du volume élémentaire représentatif qui conduit à des estimations de sa taille minimale conformes aux résultats théoriques existants. Un critère qualitatif de convergence des simulations numériques est proposé et illustré par des calculs par éléments finis.

Received: 2004-06-26
Accepted: 2004-10-05
Published online: 2005-01-07

DOI: 10.1016/j.crme.2004.10.003

Keywords: Computational solid mechanics, Homogenization, Periodization, Random media, Representative volume element
Mots-clés : Mécanique des solides numérique, Homogénéisation, Périodisation, Milieux aléatoires, Volume élémentaire représentatif

Author's affiliations:

Karam Sab ¹; Boumediene Nedjar ¹

¹ Institut Navier, LAMI, École nationale des ponts et chaussées, 6-8, avenue Blaise Pascal, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2, France

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     author = {Karam Sab and Boumediene Nedjar},
     title = {Periodization of random media and representative volume element size for linear composites},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {187--195},
     publisher = {Elsevier},
     volume = {333},
     number = {2},
     year = {2005},
     doi = {10.1016/j.crme.2004.10.003},
     language = {en},
}

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Karam Sab; Boumediene Nedjar. Periodization of random media and representative volume element size for linear composites. Comptes Rendus. Mécanique, Volume 333 (2005) no. 2, pp. 187-195. doi : 10.1016/j.crme.2004.10.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.10.003/

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