Random homogenization analysis in linear elasticity based on analytical bounds and estimates

authored by: Juan Ma, Ilker Temizer, Peter Wriggers
Abstract: In this work, random homogenization analysis of heterogeneous materials is addressed in the context of elasticity, where the randomness and correlation of components' properties are fully considered and random effective properties together with their correlation for the two-phase heterogeneous material are then sought. Based on the analytical results of homogenization in linear elasticity, when the randomness of bulk and shear moduli, the volume fraction of each constituent material and correlation among random variables are considered simultaneously, formulas of random mean values and mean square deviations of analytical bounds and estimates are derived from Random Factor Method. Results from the Random Factor Method and the Monte-Carlo Method are compared with each other through numerical examples, and impacts of randomness and correlation of random variables on the random homogenization results are inspected by two methods. Moreover, the correlation coefficients of random effective properties are obtained by the Monte-Carlo Method. The Random Factor Method is found to deliver rapid results with comparable accuracy to the Monte-Carlo approach.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Xidian University
Type: Article
Journal: International Journal of Solids and Structures
Volume: 48
Pages: 280-291
No. of pages: 12
ISSN: 0020-7683
Publication date: 10.10.2010
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, General Materials Science, Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.ijsolstr.2010.10.004 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{4e82e7b3db4240c1a8ed39a3dd150f2f,
title = "Random homogenization analysis in linear elasticity based on analytical bounds and estimates",
abstract = "In this work, random homogenization analysis of heterogeneous materials is addressed in the context of elasticity, where the randomness and correlation of components' properties are fully considered and random effective properties together with their correlation for the two-phase heterogeneous material are then sought. Based on the analytical results of homogenization in linear elasticity, when the randomness of bulk and shear moduli, the volume fraction of each constituent material and correlation among random variables are considered simultaneously, formulas of random mean values and mean square deviations of analytical bounds and estimates are derived from Random Factor Method. Results from the Random Factor Method and the Monte-Carlo Method are compared with each other through numerical examples, and impacts of randomness and correlation of random variables on the random homogenization results are inspected by two methods. Moreover, the correlation coefficients of random effective properties are obtained by the Monte-Carlo Method. The Random Factor Method is found to deliver rapid results with comparable accuracy to the Monte-Carlo approach.",
keywords = "Homogenization, Linear elasticity, Monte-Carlo Method, Random effective properties, Random Factor Method",
author = "Juan Ma and Ilker Temizer and Peter Wriggers",
year = "2010",
month = oct,
day = "10",
doi = "10.1016/j.ijsolstr.2010.10.004",
language = "English",
volume = "48",
pages = "280--291",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Ltd.",
number = "2",
}