A new mixed finite element based on different approximations of the minors of deformation tensors

authored by: Jörg Schröder, Peter Wriggers, Daniel Balzani
Abstract: Finite element formulations for arbitrary hyperelastic strain energy functions that are characterized by a locking-free behavior for incompressible materials, a good bending performance and accurate solutions for coarse meshes need still attention. Therefore, the main goal of this contribution is to provide an improved mixed finite element for quasi-incompressible finite elasticity. Based on the knowledge that the minors of the deformation gradient play a major role for the transformation of infinitesimal line-, area- and volume elements, as well as in the formulation of polyconvex strain energy functions a mixed finite element with different interpolation orders of the terms related to the minors is developed. Due to the formulation it is possible to condensate the mixed element formulation at element level to a pure displacement form. Examples show the performance and robustness of the element.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Duisburg-Essen
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 200
Pages: 3583-3600
No. of pages: 18
ISSN: 0045-7825
Publication date: 06.09.2011
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2011.08.009 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{b4623308035f4b2181b822d3743a7edc,
title = "A new mixed finite element based on different approximations of the minors of deformation tensors",
abstract = "Finite element formulations for arbitrary hyperelastic strain energy functions that are characterized by a locking-free behavior for incompressible materials, a good bending performance and accurate solutions for coarse meshes need still attention. Therefore, the main goal of this contribution is to provide an improved mixed finite element for quasi-incompressible finite elasticity. Based on the knowledge that the minors of the deformation gradient play a major role for the transformation of infinitesimal line-, area- and volume elements, as well as in the formulation of polyconvex strain energy functions a mixed finite element with different interpolation orders of the terms related to the minors is developed. Due to the formulation it is possible to condensate the mixed element formulation at element level to a pure displacement form. Examples show the performance and robustness of the element.",
keywords = "Anisotropy, Mixed finite elements, Polyconvexity, Quasi-incompressible elasticity",
author = "J{\"o}rg Schr{\"o}der and Peter Wriggers and Daniel Balzani",
note = "Funding information: The authors greatly appreciate the Deutsche Forschungsgemeinschaft (DFG) for the financial support under the research grant SCHR 570/7-2 .",
year = "2011",
month = sep,
day = "6",
doi = "10.1016/j.cma.2011.08.009",
language = "English",
volume = "200",
pages = "3583--3600",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
number = "49-52",
}