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

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  • Universität Duisburg-Essen
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OriginalspracheEnglisch
Aufsatznummer9
FachzeitschriftAdvanced Modeling and Simulation in Engineering Sciences
Jahrgang6
Ausgabenummer1
PublikationsstatusVeröffentlicht - 2019

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.

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An extension of assumed stress finite elements to a general hyperelastic framework. / Viebahn, Nils; Schröder, Jörg; Wriggers, Peter.
in: Advanced Modeling and Simulation in Engineering Sciences, Jahrgang 6, Nr. 1, 9, 2019.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Viebahn, N, Schröder, J & Wriggers, P 2019, 'An extension of assumed stress finite elements to a general hyperelastic framework', Advanced Modeling and Simulation in Engineering Sciences, Jg. 6, Nr. 1, 9. https://doi.org/10.1186/s40323-019-0133-z
Viebahn, N., Schröder, J., & Wriggers, P. (2019). An extension of assumed stress finite elements to a general hyperelastic framework. Advanced Modeling and Simulation in Engineering Sciences, 6(1), Artikel 9. https://doi.org/10.1186/s40323-019-0133-z
Viebahn N, Schröder J, Wriggers P. An extension of assumed stress finite elements to a general hyperelastic framework. Advanced Modeling and Simulation in Engineering Sciences. 2019;6(1):9. doi: 10.1186/s40323-019-0133-z
Viebahn, Nils ; Schröder, Jörg ; Wriggers, Peter. / An extension of assumed stress finite elements to a general hyperelastic framework. in: Advanced Modeling and Simulation in Engineering Sciences. 2019 ; Jahrgang 6, Nr. 1.
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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.",
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AU - Schröder, Jörg

AU - Wriggers, Peter

N1 - 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.

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