A macro-element for incompressible finite deformations based on a volume averaged deformation gradient

verfasst von
E. F.I. Boerner, Peter Wriggers
Abstract

A three-dimensional 8-node brick continuum finite element formulation for incompressible finite elasticity is presented. The core idea is to introduce a substructure consisting of eight sub-elements inside each finite element, further referred to as macro-element. For each of the sub-elements, the deformation is averaged. The weak form for each sub-element is based on the Hu-Washizu principle. The response of each sub-element is assembled and projected onto the eight external nodes of the macro-element. The introduction of deformable sub-elements in case of incompressible elasticity has two major advantages. Firstly, it is possible to suppress locking by evaluating the volumetric part of the response only in the macro-element instead of in each of the sub-elements. Secondly, no integration is necessary due to the use of averaged deformations on the sub-element level. The idea originates from the Cosserat point element developed in Nadler and Rubin (Int J Solids Struct 40:4585-4614, 2003). A consistent transition between the Cosserat point macro-element and a displacement macro-element formulation using a kinematical description from the enhanced strain element formulation (Flanagan, Belytschko in Int J Numer Methods Eng 17:679-706, 1981) or (Belytschko et al. in Comput Methods Appl Mech Eng 43:251-276, 1984) and the principle of Hu-Washizu is presented. The performance is examined by means of numerical examples.

Organisationseinheit(en)
Institut für Kontinuumsmechanik
Typ
Artikel
Journal
Computational mechanics
Band
42
Seiten
407-416
Anzahl der Seiten
10
ISSN
0178-7675
Publikationsdatum
07.03.2008
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Numerische Mechanik, Meerestechnik, Maschinenbau, Theoretische Informatik und Mathematik, Computational Mathematics, Angewandte Mathematik
Elektronische Version(en)
https://doi.org/10.1007/s00466-008-0250-x (Zugang: Unbekannt)
 

Details im Forschungsportal „Research@Leibniz University“