Details
| Original language | English |
|---|---|
| Pages (from-to) | 280-291 |
| Number of pages | 12 |
| Journal | International Journal of Solids and Structures |
| Volume | 48 |
| Issue number | 2 |
| Publication status | Published - 10 Oct 2010 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Materials Science(all)
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal of Solids and Structures, Vol. 48, No. 2, 10.10.2010, p. 280-291.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Random homogenization analysis in linear elasticity based on analytical bounds and estimates
AU - Ma, Juan
AU - Temizer, Ilker
AU - Wriggers, Peter
PY - 2010/10/10
Y1 - 2010/10/10
N2 - 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.
AB - 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.
KW - Homogenization
KW - Linear elasticity
KW - Monte-Carlo Method
KW - Random effective properties
KW - Random Factor Method
UR - http://www.scopus.com/inward/record.url?scp=78249289105&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2010.10.004
DO - 10.1016/j.ijsolstr.2010.10.004
M3 - Article
AN - SCOPUS:78249289105
VL - 48
SP - 280
EP - 291
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
SN - 0020-7683
IS - 2
ER -