An adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures

authored by: I. Temizer, P. Wriggers
Abstract: Standard homogenized formulations of problems posed on microheterogeneous domains provide a lower order of accuracy in regions where highly localized variations are observed in the solution fields. In order to account for this loss of accuracy for the finite deformation analysis of generally inelastic macrostructures, a scale adaptation strategy is developed where a transition from a homogenized description to an explicit microstructural resolution is pursued in designated zones of interest. Motivated by higher-order homogenization techniques, the adaptation zones are identified based on a post-processing step on the homogenized solution and correspond to regions with high strain-gradients. In order to avoid modeling errors emanating from the use of approximate explicit macroscale constitutive formulations, an exact homogenization procedure based on databased and direct multilevel finite element computations is employed. The overall methodology is investigated in a two-dimensional setting where special attention is paid to the underlying multiscale mesh resolution and additionally demonstrated with a three-dimensional problem. Numerical observations suggest the concept of a representative adaptation zone within which scale adaptation effects can be assessed.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 200
Pages: 2639-2661
No. of pages: 23
ISSN: 0045-7825
Publication date: 13.06.2010
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2010.06.013 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{2ef427dfa676470ca93f57b7e64f39bc,
title = "An adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures",
abstract = "Standard homogenized formulations of problems posed on microheterogeneous domains provide a lower order of accuracy in regions where highly localized variations are observed in the solution fields. In order to account for this loss of accuracy for the finite deformation analysis of generally inelastic macrostructures, a scale adaptation strategy is developed where a transition from a homogenized description to an explicit microstructural resolution is pursued in designated zones of interest. Motivated by higher-order homogenization techniques, the adaptation zones are identified based on a post-processing step on the homogenized solution and correspond to regions with high strain-gradients. In order to avoid modeling errors emanating from the use of approximate explicit macroscale constitutive formulations, an exact homogenization procedure based on databased and direct multilevel finite element computations is employed. The overall methodology is investigated in a two-dimensional setting where special attention is paid to the underlying multiscale mesh resolution and additionally demonstrated with a three-dimensional problem. Numerical observations suggest the concept of a representative adaptation zone within which scale adaptation effects can be assessed.",
keywords = "Homogenization, Multiscale analysis, Scale adaptivity",
author = "I. Temizer and P. Wriggers",
note = "Funding information: Support for this work was provided by the German Research Foundation (DFG) under Grant No. WR 19/36-1 . The assistance of Christian Wei{\ss}enfels in the numerical example involving the 27-node hexahedral element is much appreciated.",
year = "2010",
month = jun,
day = "13",
doi = "10.1016/j.cma.2010.06.013",
language = "English",
volume = "200",
pages = "2639--2661",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
number = "37-40",
}