A domain decomposition method for bodies with heterogeneous microstructure basedon material regularization

authored by: T. Zohdi, Peter Wriggers
Abstract: A domain decomposition methodis developed to reduce the computational complexity of boundary value problems associated withthe structural analysis of bodies with arbitrary external geometry, loading and linearly elasticmicrostructure. The purpose of the method is to augment existing numerical discretizationmethods of analysis, such as the finite element method. The approach is to partition and decouplethe heterogeneous body into more computationally tractable, nonoverlapping, subdomains whoseunion forms the entire domain under analysis. This is achieved by approximating the subdomainboundary conditions. The approximate boundary conditions, of displacement or traction type, aresupplied from the solution to a relatively computationally inexpensive auxiliary boundary valueproblem characterized by a simple regularized microstructure. Since the decoupled subdomainsmay then be analyzed separately, the memory requirements are reduced and computingprocedures are trivially parallelizable. A-posteriori error bounds are developed for solutionsgenerated by this process. It is shown that, in the special case of uniform exterior loading, theerror bounds collapse into forms which imply results pertaining to effective property orderingcoinciding with those published by .
Organisation(s): Institute of Mechanics and Computational Mechanics
Type: Article
Journal: International Journal of Solids and Structures
Volume: 36
Pages: 2507-2525
No. of pages: 19
ISSN: 0020-7683
Publication date: 12.05.1999
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Materials Science(all), Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/S0020-7683(98)00124-3 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{0e99c20a102a402e9cbdb41d39a4a1ff,
title = "A domain decomposition method for bodies with heterogeneous microstructure basedon material regularization",
abstract = "A domain decomposition methodis developed to reduce the computational complexity of boundary value problems associated withthe structural analysis of bodies with arbitrary external geometry, loading and linearly elasticmicrostructure. The purpose of the method is to augment existing numerical discretizationmethods of analysis, such as the finite element method. The approach is to partition and decouplethe heterogeneous body into more computationally tractable, nonoverlapping, subdomains whoseunion forms the entire domain under analysis. This is achieved by approximating the subdomainboundary conditions. The approximate boundary conditions, of displacement or traction type, aresupplied from the solution to a relatively computationally inexpensive auxiliary boundary valueproblem characterized by a simple regularized microstructure. Since the decoupled subdomainsmay then be analyzed separately, the memory requirements are reduced and computingprocedures are trivially parallelizable. A-posteriori error bounds are developed for solutionsgenerated by this process. It is shown that, in the special case of uniform exterior loading, theerror bounds collapse into forms which imply results pertaining to effective property orderingcoinciding with those published by .",
author = "T. Zohdi and Peter Wriggers",
year = "1999",
month = may,
day = "12",
doi = "10.1016/S0020-7683(98)00124-3",
language = "English",
volume = "36",
pages = "2507--2525",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Ltd.",
number = "17",
}