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Multi-scale Simulation of Composite MaterialsIndicators for the Adaptive Choice of Multi-Scale Solvers Based on Configurational Mechanics

Multi-scale Simulation of Composite Materials: Indicators for the Adaptive Choice of Multi-Scale... [For heterogeneous multi-scale methods,Methodmulti-scaledifferent analytical and numerical homogenisation methodsHomogenisation can be applied on the micro-level, where the computational domain is a representative volume element (RVE). Several numerical homogenisation algorithms which are based on boundary element approaches, Boundary elementpseudo spectral discretizations, or finite element schemes are available for RVEs. MethodBoundary ElementHowever, each of these methods is onlyMethodpseudo spectral appropriate in subdomainsMethodFinite Element of the macro-scale domain (component), e.g. in low-stress or highly stressed component regions. Therefore, indicators for the adaptive choice of solvers on the micro-scale are helpful. The proposed indicators make use of ideas from configurational mechanics.ConfigurationalmechanicsFirst of all, configurational forcesConfigurationalforces are introduced as indicators. Then the multi-scale approachMulti-scaleapproach for configurational forces is explained and illustrated with an example. Afterwards the application of the configurational forces as an indicator for a refined homogenisation methodMethodhomogenisation is demonstrated. The last section is devoted to the scalability of heterogeneous multi-scale computationsMulti-scalecomputations on parallel computersParallelcomputers. A parallel finite element codeParallelfinite element code is used for the macro-scale, and a PYTHON interface for the coupling with the different micro-scale solvers is described.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Multi-scale Simulation of Composite MaterialsIndicators for the Adaptive Choice of Multi-Scale Solvers Based on Configurational Mechanics

Part of the Mathematical Engineering Book Series
Editors: Diebels, Stefan; Rjasanow, Sergej
Müller, Ralf; Kuhn, Charlotte; Klassen, Markus; Andrä, Heiko; Staub, Sarah
Multi-scale Simulation of Composite Materials — Feb 2, 2019
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15 pages

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References (28)

Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag GmbH Germany, part of Springer Nature 2019
ISBN
978-3-662-57956-5
Pages
15 –30
DOI
10.1007/978-3-662-57957-2_2
Publisher site
See Chapter on Publisher Site

Abstract

[For heterogeneous multi-scale methods,Methodmulti-scaledifferent analytical and numerical homogenisation methodsHomogenisation can be applied on the micro-level, where the computational domain is a representative volume element (RVE). Several numerical homogenisation algorithms which are based on boundary element approaches, Boundary elementpseudo spectral discretizations, or finite element schemes are available for RVEs. MethodBoundary ElementHowever, each of these methods is onlyMethodpseudo spectral appropriate in subdomainsMethodFinite Element of the macro-scale domain (component), e.g. in low-stress or highly stressed component regions. Therefore, indicators for the adaptive choice of solvers on the micro-scale are helpful. The proposed indicators make use of ideas from configurational mechanics.ConfigurationalmechanicsFirst of all, configurational forcesConfigurationalforces are introduced as indicators. Then the multi-scale approachMulti-scaleapproach for configurational forces is explained and illustrated with an example. Afterwards the application of the configurational forces as an indicator for a refined homogenisation methodMethodhomogenisation is demonstrated. The last section is devoted to the scalability of heterogeneous multi-scale computationsMulti-scalecomputations on parallel computersParallelcomputers. A parallel finite element codeParallelfinite element code is used for the macro-scale, and a PYTHON interface for the coupling with the different micro-scale solvers is described.]

Published: Feb 2, 2019

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