An extension of assumed stress finite elements to a general hyperelastic framework

authored by: Nils Viebahn, Jörg Schröder, Peter Wriggers
Abstract: Assumed stress finite elements are known for their extraordinary good performance in the framework of linear elasticity. In this contribution we propose a mixed variational formulation of the Hellinger–Reissner type for hyperelasticity. A family of hexahedral shaped elements is considered with a classical trilinear interpolation of the displacements and different piecewise discontinuous interpolation schemes for the stresses. The performance and stability of the new elements are investigated and demonstrated by the analysis of several benchmark problems. In addition the results are compared to well known enhanced assumed strain elements.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Duisburg-Essen
Type: Article
Journal: Advanced Modeling and Simulation in Engineering Sciences
Volume: 6
Publication date: 2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Engineering (miscellaneous), Computer Science Applications, Applied Mathematics
Electronic version(s): https://doi.org/10.1186/s40323-019-0133-z (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{15beae2cdaad4b71a94f56098efd71b5,
title = "An extension of assumed stress finite elements to a general hyperelastic framework",
abstract = "Assumed stress finite elements are known for their extraordinary good performance in the framework of linear elasticity. In this contribution we propose a mixed variational formulation of the Hellinger–Reissner type for hyperelasticity. A family of hexahedral shaped elements is considered with a classical trilinear interpolation of the displacements and different piecewise discontinuous interpolation schemes for the stresses. The performance and stability of the new elements are investigated and demonstrated by the analysis of several benchmark problems. In addition the results are compared to well known enhanced assumed strain elements.",
keywords = "Assumed stress element, Hellinger–Reissner formulation, Hourglassing, Hyperelasticity, Locking free, Mixed FEM, Nearly incompressibility",
author = "Nils Viebahn and J{\"o}rg Schr{\"o}der and Peter Wriggers",
note = "Funding information: The authors appreciate the support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Novel finite elements - Mixed, Hybrid and Virtual Element formulations at finite strains for 3D applications” under the project “Reliable Simulation Techniques in Solid Mechanics, Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis” (SCHR 570/23-2) (WR 19/50-2). Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 255432295. We acknowledge support by the Open Access Publication Fund of the University of Duisburg-Essen.",
year = "2019",
doi = "10.1186/s40323-019-0133-z",
language = "English",
volume = "6",
journal = "Advanced Modeling and Simulation in Engineering Sciences",
issn = "2213-7467",
publisher = "Springer Open",
number = "1",
}