Details
| Original language | English |
|---|---|
| Pages (from-to) | 3583-3600 |
| Number of pages | 18 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 200 |
| Issue number | 49-52 |
| Publication status | Published - 6 Sept 2011 |
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
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Computer Methods in Applied Mechanics and Engineering, Vol. 200, No. 49-52, 06.09.2011, p. 3583-3600.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A new mixed finite element based on different approximations of the minors of deformation tensors
AU - Schröder, Jörg
AU - Wriggers, Peter
AU - Balzani, Daniel
N1 - Funding information: The authors greatly appreciate the Deutsche Forschungsgemeinschaft (DFG) for the financial support under the research grant SCHR 570/7-2 .
PY - 2011/9/6
Y1 - 2011/9/6
N2 - 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.
AB - 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.
KW - Anisotropy
KW - Mixed finite elements
KW - Polyconvexity
KW - Quasi-incompressible elasticity
UR - http://www.scopus.com/inward/record.url?scp=80053527560&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2011.08.009
DO - 10.1016/j.cma.2011.08.009
M3 - Article
AN - SCOPUS:80053527560
VL - 200
SP - 3583
EP - 3600
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
IS - 49-52
ER -