Further Insights by Theoretical Investigations of the Multiscale Arlequin Method

Hachmi Ben Dhia · International Journal for Multiscale Computational Engineering · 2008

Summary

The Arlequin method allows for concurrent multimodel and multiscale analyses of mechanical problems and is helpful for the design of reliable choices.

Type: article
Published: 2008-01-01
Cited by: 76
References: 22
Access: Open access
DOI: https://doi.org/10.1615/intjmultcompeng.v6.i3.30
OpenAlex: https://openalex.org/W1985625692
Semantic Scholar: https://api.semanticscholar.org/CorpusID:60874459

Keywords

Simple (philosophy), Computer science, Applied mathematics, Mathematics, Epistemology

References

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Elliptic Problems in Nonsmooth DomainsPierre Grisvard — 1985
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A Force-Based Blending Model forAtomistic-to-Continuum CouplingSantiago Badia, Pavel Bochev, Richard B. Lehoucq — 2007
On the L2 and the H1 couplings for an overlapping domain decomposition method using Lagrange multipliersPierre‐Alain Guidault, Ted Belytschko — 2007
The Arlequin method as a flexible engineering design toolH. Ben Dhia, Guillaume Rateau — 2005
Application of the Arlequin method to some structures with defectsHachmi Ben Dhia, Guillaume Rateau — 2002
Book Reviews : The Finite Element Method (Revised): O.C. Zienkiewicz McGraw-Hill Book Co., New York, New YorkH. Saunders — 1980
Error-bounds for finite element methodIvo Babuška — 1971
Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin methodSerge Prudhomme, H. Ben Dhia, Paul T. Bauman — 2008
Global-local approaches: the Arlequin frameworkHachmi Ben Dhia — 2006
Analyse mathématique de la méthode Arlequin mixteHachmi Ben Dhia, Guillaume Rateau — 2001
Level-Sets and Arlequin framework for dynamic contact problemsHachmi Ben Dhia, Chokri Zammali — 2004
From Molecular Models¶to Continuum MechanicsXavier Blanc, Claude Le Bris, Pierre Louis Lions — 2002
The finite element method for elliptic problemsPhilippe G. Ciarlet — 2002
A bridging domain method for coupling continua with molecular dynamicsShaoping Xiao, Ted Belytschko — 2004
On the application of the Arlequin method to the coupling of particle and continuum modelsPaul T. Bauman, Hachmi Ben Dhia, Nadia Elkhodja — 2008
Multiscale mechanical problems: the Arlequin methodHachmi Ben Dhia — 1998
Coupling of atomistic and continuum models in the Arlequin frameworkHachmi Ben Dhia, Nadia Elkhodja — 2007

Cited by

Propagation numérique de zones critiques dans un pneumatique par approches multi-modèlesOlivier Jamond — 2011
Contributions à la modélisation avancée des machines tournantes en dynamique transitoire dans le cadre ArlequinAssaf Ghanem — 2013
Approches numérique multi-échelle/multi-modèle de la dégradation des matériaux compositesJ. Touzeau — 2012
Modelling-based design of anisotropic piezocomposite transducers and multi-domain analysis of smart structuresFabio Biscani — 2012
Numerical strategy for unbiased homogenization of random materialsRégis Cottereau — 2013
Heterogeneous asynchronous time integrators for computational structural dynamicsAnthony Gravouil, Alain Combescure, M. Brun — 2015
Error estimation and model adaptation for a stochastic‐deterministic coupling method based on the Arlequin frameworkCédric Zaccardi, Ludovic Chamoin, Régis Cottereau — 2013
Variable kinematic plate elements coupled via Arlequin methodFabio Biscani, Gaetano Giunta, Salim Belouettar — 2012
Coupling of nonlocal and local continuum models by the Arlequin approachFei Han, Gilles Lubineau — 2012
Incompressibility in the multimodel Arlequin frameworkOlivier Jamond, Hachmi Ben Dhia — 2013
On the use of XFEM within the Arlequin framework for the simulation of crack propagationHachmi Ben Dhia, Olivier Jamond — 2010
A Stochastic-deterministic Coupling Method for Multiscale Problems. Application to Numerical Homogenization of Random Materials☆Régis Cottereau — 2013
Bridging techniques in a multi-scale modeling of pattern formationFan Xu, Heng Hu, Michel Potier‐Ferry — 2014
Modeling and computation of fretting wear of structures under sharp contactHachmi Ben Dhia, Mohamed Torkhani — 2011
Multi-scale techniques to analyze instabilities in sandwich structuresKun Yu, Heng Hu, Siyu Chen — 2013
A stochastic-deterministic coupling method for continuum mechanicsRégis Cottereau, Didier Clouteau, Hachmi Ben Dhia — 2011
A bridging technique to analyze the influence of boundary conditions on instability patternsHeng Hu, Noureddine Damil, Michel Potier‐Ferry — 2011
Arlequin based PGD domain decompositionS. Mohamed Nazeer, Felipe Bordeu, Adrien Leygue — 2014
Ghost forces and spurious effects in atomic‐to‐continuum coupling methods by the Arlequin approachLudovic Chamoin, Serge Prudhomme, Hachmi Ben Dhia — 2010
Multiscale Modeling of Complex Dynamic Problems: An Overview and Recent DevelopmentsMohamed Jebahi, Frédéric Dau, Jean‐Luc Charles — 2016

Further Insights by Theoretical Investigations of the Multiscale Arlequin Method

Summary

Keywords

References

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