Details
| Original language | English |
|---|---|
| Article number | 9 |
| Journal | Advanced Modeling and Simulation in Engineering Sciences |
| Volume | 6 |
| Issue number | 1 |
| Publication status | Published - 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.
Keywords
- Assumed stress element, Hellinger–Reissner formulation, Hourglassing, Hyperelasticity, Locking free, Mixed FEM, Nearly incompressibility
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Engineering (miscellaneous)
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Advanced Modeling and Simulation in Engineering Sciences, Vol. 6, No. 1, 9, 2019.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An extension of assumed stress finite elements to a general hyperelastic framework
AU - Viebahn, Nils
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.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Assumed stress element
KW - Hellinger–Reissner formulation
KW - Hourglassing
KW - Hyperelasticity
KW - Locking free
KW - Mixed FEM
KW - Nearly incompressibility
UR - http://www.scopus.com/inward/record.url?scp=85066396613&partnerID=8YFLogxK
U2 - 10.1186/s40323-019-0133-z
DO - 10.1186/s40323-019-0133-z
M3 - Article
AN - SCOPUS:85066396613
VL - 6
JO - Advanced Modeling and Simulation in Engineering Sciences
JF - Advanced Modeling and Simulation in Engineering Sciences
IS - 1
M1 - 9
ER -