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An FE²-X¹ approach for multiscale localization phenomena

  • In this paper, a new methodology based on the Hill–Mandel lemma in an FE² sense is proposed that is able to deal with localized deformations. This is achieved by decomposing the displacement field of the fine scale model into a homogeneous part, fluctuations, and a cracking part based on additional degrees of freedom (X¹)—the crack opening in normal and tangential directions. Based on this decomposition, the Hill–Mandel lemma is extended to relate coarse and fine scale energies using the assumption of separation of scales such that the fine scale model is not required to have the same size as the corresponding macroscopic integration point. In addition, a procedure is introduced to mimic periodic boundary conditions in the linear elastic range by adding additional shape functions for the boundary nodes that represent the difference between periodic boundary conditions and pure displacement boundary conditions due to the same macroscopic strain. In order to decrease theIn this paper, a new methodology based on the Hill–Mandel lemma in an FE² sense is proposed that is able to deal with localized deformations. This is achieved by decomposing the displacement field of the fine scale model into a homogeneous part, fluctuations, and a cracking part based on additional degrees of freedom (X¹)—the crack opening in normal and tangential directions. Based on this decomposition, the Hill–Mandel lemma is extended to relate coarse and fine scale energies using the assumption of separation of scales such that the fine scale model is not required to have the same size as the corresponding macroscopic integration point. In addition, a procedure is introduced to mimic periodic boundary conditions in the linear elastic range by adding additional shape functions for the boundary nodes that represent the difference between periodic boundary conditions and pure displacement boundary conditions due to the same macroscopic strain. In order to decrease the computational effort, an adaptive strategy is proposed allowing different macroscopic integration points to be resolved in different levels on the fine scale.zeige mehrzeige weniger

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Metadaten
Autor*innen:Jörg F. UngerORCiD
Dokumenttyp:Zeitschriftenartikel
Veröffentlichungsform:Verlagsliteratur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):Journal of the Mechanics and Physics of Solids
Jahr der Erstveröffentlichung:2013
Verlag:Elsevier
Jahrgang/Band:61
Ausgabe/Heft:4
Erste Seite:928
Letzte Seite:948
DDC-Klassifikation:Technik, Medizin, angewandte Wissenschaften / Ingenieurwissenschaften / Ingenieurbau
Freie Schlagwörter:Constitutive behavior; Finite elements; Fracture; Inhomogeneous material; Multiscale
DOI:10.1016/j.jmps.2012.12.010
ISSN:0022-5096
Verfügbarkeit des Dokuments:Datei im Netzwerk der BAM verfügbar ("Closed Access")
Datum der Freischaltung:02.05.2016
Referierte Publikation:Ja
Datum der Eintragung als referierte Publikation:14.12.2016
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