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

authored by: 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.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computational mechanics
Volume: 42
Pages: 407-416
No. of pages: 10
ISSN: 0178-7675
Publication date: 07.03.2008
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-008-0250-x (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{68c033cb3a254d3499f023c2b16c9e72,
title = "A macro-element for incompressible finite deformations based on a volume averaged deformation gradient",
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.",
keywords = "Finite elasticity, Finite element technology, Incompressibility",
author = "Boerner, {E. F.I.} and Peter Wriggers",
year = "2008",
month = mar,
day = "7",
doi = "10.1007/s00466-008-0250-x",
language = "English",
volume = "42",
pages = "407--416",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "3",
}