Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure

authored by: Juan Ma, Shahab Sahraee, Peter Wriggers, Laura De Lorenzis
Abstract: In this work, stochastic homogenization analysis of heterogeneous materials is addressed in the context of elasticity under finite deformations. The randomness of the morphology and of the material properties of the constituents as well as the correlation among these random properties are fully accounted for, and random effective quantities such as tangent tensor, first Piola–Kirchhoff stress, and strain energy along with their numerical characteristics are tackled under different boundary conditions by a multiscale finite element strategy combined with the Montecarlo method. The size of the representative volume element (RVE) with randomly distributed particles for different particle volume fractions is first identified by a numerical convergence scheme. Then, different types of displacement-controlled boundary conditions are applied to the RVE while fully considering the uncertainty in the microstructure. The influence of different random cases including correlation on the random effective quantities is finally analyzed.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Xidian University
Technische Universität Braunschweig
Type: Article
Journal: Computational mechanics
Volume: 55
Pages: 819-835
No. of pages: 17
ISSN: 0178-7675
Publication date: 31.03.2015
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-015-1136-3 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{d443d43b912b4bd0b5a36e3355ecd738,
title = "Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure",
abstract = "In this work, stochastic homogenization analysis of heterogeneous materials is addressed in the context of elasticity under finite deformations. The randomness of the morphology and of the material properties of the constituents as well as the correlation among these random properties are fully accounted for, and random effective quantities such as tangent tensor, first Piola–Kirchhoff stress, and strain energy along with their numerical characteristics are tackled under different boundary conditions by a multiscale finite element strategy combined with the Montecarlo method. The size of the representative volume element (RVE) with randomly distributed particles for different particle volume fractions is first identified by a numerical convergence scheme. Then, different types of displacement-controlled boundary conditions are applied to the RVE while fully considering the uncertainty in the microstructure. The influence of different random cases including correlation on the random effective quantities is finally analyzed.",
keywords = "Finite deformations, Montecarlo method, Multiscale analysis, Randomness and correlation, Stochastic homogenization",
author = "Juan Ma and Shahab Sahraee and Peter Wriggers and {De Lorenzis}, Laura",
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 (11102143) is also sincerely acknowledged. The first author would like to acknowledge Professor Ilker Temizer for his code of lecture “Micromechanics” at Leibniz Universit{\"a}t Hannover as well. L. De Lorenzis would like to acknowledge the European Research Council, ERC Starting Researcher Grant “INTERFACES”, Grant Agreement N. 279439.",
year = "2015",
month = mar,
day = "31",
doi = "10.1007/s00466-015-1136-3",
language = "English",
volume = "55",
pages = "819--835",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "5",
}