Random homogenization analysis for heterogeneous materials with full randomness and correlation in microstructure based on finite element method and Monte-carlo method

authored by: Juan Ma, Jie Zhang, Liangjie Li, Peter Wriggers, Shahab Sahraee
Abstract: The computationally random homogenization analysis of a two-phase heterogeneous materials is addressed in the context of linear elasticity where the randomness of constituents’ moduli and microstructural morphology together with the correlation among random moduli are fully considered, and random effective quantities such as effective elastic tensor and effective stress as well as effective strain energy together with their numerical characteristics are then sought for different boundary conditions. Based on the finite element method and Monte-carlo method, the RVE with randomly distributing particles determined by a numerical convergence scheme is firstly generated and meshed, and two types of boundary conditions controlled by average strain are then applied to the RVE where the uncertainty existing in the microstructure is accounted for simultaneously. The numerical characteristics of random effective quantities such as coefficients of variation and correlation coefficients are then evaluated, and impacts of different factors on random effective quantities are finally investigated and revealed as well.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Xidian University
Type: Article
Journal: Computational mechanics
Volume: 54
Pages: 1395-1414
No. of pages: 20
ISSN: 0178-7675
Publication date: 12.2014
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-014-1065-6 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{adbf0a871b7649d5afb8dae8f1f6d107,
title = "Random homogenization analysis for heterogeneous materials with full randomness and correlation in microstructure based on finite element method and Monte-carlo method",
abstract = "The computationally random homogenization analysis of a two-phase heterogeneous materials is addressed in the context of linear elasticity where the randomness of constituents{\textquoteright} moduli and microstructural morphology together with the correlation among random moduli are fully considered, and random effective quantities such as effective elastic tensor and effective stress as well as effective strain energy together with their numerical characteristics are then sought for different boundary conditions. Based on the finite element method and Monte-carlo method, the RVE with randomly distributing particles determined by a numerical convergence scheme is firstly generated and meshed, and two types of boundary conditions controlled by average strain are then applied to the RVE where the uncertainty existing in the microstructure is accounted for simultaneously. The numerical characteristics of random effective quantities such as coefficients of variation and correlation coefficients are then evaluated, and impacts of different factors on random effective quantities are finally investigated and revealed as well.",
keywords = "Finite element method, Linear elasticity, Monte-carlo method, Random homogenization, Randomness and correlation",
author = "Juan Ma and Jie Zhang and Liangjie Li and Peter Wriggers and Shahab Sahraee",
note = "Funding information: The first author gratefully acknowledges the support of the Alexander von Humboldt Stiftung through a {\textquoteleft}Humboldt Research Fellowship for Postdoctoral Researchers{\textquoteright} for a research stay at the Leibniz Universit{\"a}t Hannover. The support of Natural Science Foundation of China to the project (JJ0500110405) “Random homogenization of heterogeneous materials with infinitesimal and finite deformation” is also gratefully acknowledged.",
year = "2014",
month = dec,
doi = "10.1007/s00466-014-1065-6",
language = "English",
volume = "54",
pages = "1395--1414",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "6",
}