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Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions

hal.structure.identifierInstitut de Recherche en Génie Civil et Mécanique [GeM]
dc.contributor.authorLAMARI, Hajer
hal.structure.identifierLaboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
dc.contributor.authorAMMAR, Amine
hal.structure.identifierInstitut de Recherche en Génie Civil et Mécanique [GeM]
dc.contributor.authorCARTRAUD, Patrice
hal.structure.identifierInstitut de Recherche en Génie Civil et Mécanique [GeM]
dc.contributor.authorLEGRAIN, Grégory
hal.structure.identifierInstitut de Recherche en Génie Civil et Mécanique [GeM]
dc.contributor.authorCHINESTA, Francisco
hal.structure.identifierInstitut de Recherche en Génie Civil et Mécanique [GeM]
dc.contributor.authorJACQUEMIN, Frédéric
dc.date.accessioned2021-05-14T09:50:55Z
dc.date.available2021-05-14T09:50:55Z
dc.date.issued2010
dc.identifier.issn1134-3060
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/77333
dc.description.abstractEnComputational homogenization is nowadays one of the most active research topics in computational mechanics. Different strategies have been proposed, the main challenge being the computing cost induced by complex microstructures exhibiting nonlinear behaviors. Two quite tricky scenarios lie in (i) the necessity of applying the homogenization procedure for many microstructures (e.g. material microstructure evolving at the macroscopic level or stochastic microstructure); the second situation concerns the homogenization of nonlinear behaviors implying the necessity of solving microscopic problems for each macroscopic state (history independent nonlinear models) or for each macroscopic history (history dependant non-linear models). In this paper we present some preliminary results concerning the application of Proper Generalized Decompositions for addressing the efficient solution of homogenization problems. This numerical technique could allow to compute the homogenized properties for any microstructure or for any macroscopic loading history by solving a single but highly multidimensional model. The PGD allows circumventing the so called curse of dimensionality that mesh based representations suffer. Even if this work only describes the firs steps in a very ambitious objective , many original ideas are launched that could be at the origin of impressive progresses.
dc.language.isoen
dc.publisherSpringer Verlag
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.title.enRoutes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions
dc.typeArticle de revue
dc.identifier.doi10.1007/s11831-010-9051-4
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]
bordeaux.journalArchives of Computational Methods in Engineering
bordeaux.page373–391
bordeaux.volume17
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-01528268
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01528268v1
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