On the sensitivity of homogenized material responses at infinitesimal and finite strains

authored by: T. I. Zohdi, Peter Wriggers
Abstract: On a practical level, when computing macroscopic or homogenized mechanical responses of materials possessing heterogeneous irregular microstructure, one can only test finite-sized samples. The macroscopic responses computed from various equal finite-sized samples exhibit deviations from one another. Consequently, any use of such data afterwards contains a degree of uncertainty. For example, certain classes of finite deformation response functions such as compressible Neo-Hookean functions, compressible Mooney-Rivlin functions, and others, employ predetermined linear elastic coefficients in parts of their representations. Therefore, they will contain the mentioned uncertainties. In this work we study the magnitude of deviations between computed homogenized linearly elastic responses among equal finite sized, samples possessing random microstructure. Afterwards, the sensitivity of finite deformation response functions to such deviations is addressed. The primary result is that deviations of the responses in the infinitesimal range bound the resulting perturbed response in the finite deformation range from above.
Organisation(s): Institute of Mechanics and Computational Mechanics
Type: Article
Journal: Communications in Numerical Methods in Engineering
Volume: 16
Pages: 657-670
No. of pages: 14
ISSN: 1069-8299
Publication date: 18.08.2000
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Modelling and Simulation, General Engineering, Computational Theory and Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1002/1099-0887(200009)16:9<657::AID-CNM365>3.0.CO;2-S (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{019a7a3a26e643dd88eef191a4933f0c,
title = "On the sensitivity of homogenized material responses at infinitesimal and finite strains",
abstract = "On a practical level, when computing macroscopic or homogenized mechanical responses of materials possessing heterogeneous irregular microstructure, one can only test finite-sized samples. The macroscopic responses computed from various equal finite-sized samples exhibit deviations from one another. Consequently, any use of such data afterwards contains a degree of uncertainty. For example, certain classes of finite deformation response functions such as compressible Neo-Hookean functions, compressible Mooney-Rivlin functions, and others, employ predetermined linear elastic coefficients in parts of their representations. Therefore, they will contain the mentioned uncertainties. In this work we study the magnitude of deviations between computed homogenized linearly elastic responses among equal finite sized, samples possessing random microstructure. Afterwards, the sensitivity of finite deformation response functions to such deviations is addressed. The primary result is that deviations of the responses in the infinitesimal range bound the resulting perturbed response in the finite deformation range from above.",
author = "Zohdi, {T. I.} and Peter Wriggers",
year = "2000",
month = aug,
day = "18",
doi = "10.1002/1099-0887(200009)16:9<657::AID-CNM365>3.0.CO;2-S",
language = "English",
volume = "16",
pages = "657--670",
journal = "Communications in Numerical Methods in Engineering",
issn = "1069-8299",
publisher = "Wiley-Blackwell",
number = "9",
}