Multiscale finite element analysis of uncertain-but-bounded heterogeneous materials at finite deformation

authored by: Juan Ma, Wenyi Du, Wei Gao, Peter Wriggers, Xiangdong Xue
Abstract: A new computationally interval homogenization modelling for heterogeneous materials with uncertain-but-bounded parameters is presented in a deformation controlled setting, and the homogenization analysis in the context of elasticity at finite deformation is then addressed by an integrative approach of finite element method with the optimization algorithms where the interval uncertainty in the microstructure of the material is fully considered. Different deformation-controlled boundary conditions are imposed on the representative volume element, and the interval effective quantities involving the tangent tensor and the first Piola–Kirchhoff stress tensor as well as the strain energy together with the effective moduli are obtained. The influences of different uncertain cases on the interval effective quantities are also analyzed. For the purpose of verification, the results from particle swarm optimization (PSO) algorithm are compared with those obtained from genetic algorithm (GA) and Monte-carlo simulation. The feasibility and validity of the proposed modelling method are evidenced by the well-agreed consequences among the above algorithms.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Xidian University
University of New South Wales (UNSW)
Type: Article
Journal: Finite Elements in Analysis and Design
Volume: 149
Pages: 15-31
No. of pages: 17
ISSN: 0168-874X
Publication date: 05.07.2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Analysis, Engineering(all), Computer Graphics and Computer-Aided Design, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.finel.2018.06.001 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{5ab380daa0614e1da726a526c2c3de90,
title = "Multiscale finite element analysis of uncertain-but-bounded heterogeneous materials at finite deformation",
abstract = "A new computationally interval homogenization modelling for heterogeneous materials with uncertain-but-bounded parameters is presented in a deformation controlled setting, and the homogenization analysis in the context of elasticity at finite deformation is then addressed by an integrative approach of finite element method with the optimization algorithms where the interval uncertainty in the microstructure of the material is fully considered. Different deformation-controlled boundary conditions are imposed on the representative volume element, and the interval effective quantities involving the tangent tensor and the first Piola–Kirchhoff stress tensor as well as the strain energy together with the effective moduli are obtained. The influences of different uncertain cases on the interval effective quantities are also analyzed. For the purpose of verification, the results from particle swarm optimization (PSO) algorithm are compared with those obtained from genetic algorithm (GA) and Monte-carlo simulation. The feasibility and validity of the proposed modelling method are evidenced by the well-agreed consequences among the above algorithms.",
keywords = "Finite deformation, Finite element method, GA, Interval homogenization, PSO algorithm",
author = "Juan Ma and Wenyi Du and Wei Gao and Peter Wriggers and Xiangdong Xue",
note = "Funding information: The Corresponding author gratefully acknowledges the support of Natural Science Foundation of China to the projects (Grant No. 11102143 and No. 11572233 ). The support of the Alexander von Humboldt-Stiftung is sincerely acknowledged as well. The corresponding author would also like to appreciate Professor Ilker Temizer for his help about this work.",
year = "2018",
month = jul,
day = "5",
doi = "10.1016/j.finel.2018.06.001",
language = "English",
volume = "149",
pages = "15--31",
journal = "Finite Elements in Analysis and Design",
issn = "0168-874X",
publisher = "Elsevier",
}