Details
| Original language | English |
|---|---|
| Article number | 25 |
| Journal | Advanced Modeling and Simulation in Engineering Sciences |
| Volume | 3 |
| Issue number | 1 |
| Publication status | Published - 11 Aug 2016 |
Abstract
Anisotropic material with inextensible fibers introduce constraints in the mathematical formulations. This is always the case when fibers with high stiffness in a certain direction are present and a relatively weak matrix material is supporting these fibers. In numerical solution methods like the finite element method the presence of constraints—in this case associated to a possible fiber inextensibility compared to a matrix—lead to so called locking-phenomena. This can be overcome by special interpolation schemes as has been discussed extensively for volume constraints like incompressibility as well as contact constraints. For anisotropic material behaviour the most severe case is related to inextensible fibers. In this paper a mixed method is developed that can handle anisotropic materials with inextensible fibers that can be relaxed to extensible fiber behaviour. For this purpose a classical ansatz, known from the modeling of volume constraint is adopted leading stable elements that can be used in the finite strain regime.
Keywords
- Anisotropic material, Constraints, Finite element analysis, Mixed methods
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Engineering (miscellaneous)
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Applied Mathematics
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In: Advanced Modeling and Simulation in Engineering Sciences, Vol. 3, No. 1, 25, 11.08.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Finite element formulations for large strain anisotropic material with inextensible fibers
AU - Wriggers, P.
AU - Schröder, J.
AU - Auricchio, F.
N1 - Funding information: The first and second author acknowledge the support of the ”Deutsche Forschungsgemeinschaft” under contract of the SPP 1748, No. WR19/50-1 and SCHR570/23-1.
PY - 2016/8/11
Y1 - 2016/8/11
N2 - Anisotropic material with inextensible fibers introduce constraints in the mathematical formulations. This is always the case when fibers with high stiffness in a certain direction are present and a relatively weak matrix material is supporting these fibers. In numerical solution methods like the finite element method the presence of constraints—in this case associated to a possible fiber inextensibility compared to a matrix—lead to so called locking-phenomena. This can be overcome by special interpolation schemes as has been discussed extensively for volume constraints like incompressibility as well as contact constraints. For anisotropic material behaviour the most severe case is related to inextensible fibers. In this paper a mixed method is developed that can handle anisotropic materials with inextensible fibers that can be relaxed to extensible fiber behaviour. For this purpose a classical ansatz, known from the modeling of volume constraint is adopted leading stable elements that can be used in the finite strain regime.
AB - Anisotropic material with inextensible fibers introduce constraints in the mathematical formulations. This is always the case when fibers with high stiffness in a certain direction are present and a relatively weak matrix material is supporting these fibers. In numerical solution methods like the finite element method the presence of constraints—in this case associated to a possible fiber inextensibility compared to a matrix—lead to so called locking-phenomena. This can be overcome by special interpolation schemes as has been discussed extensively for volume constraints like incompressibility as well as contact constraints. For anisotropic material behaviour the most severe case is related to inextensible fibers. In this paper a mixed method is developed that can handle anisotropic materials with inextensible fibers that can be relaxed to extensible fiber behaviour. For this purpose a classical ansatz, known from the modeling of volume constraint is adopted leading stable elements that can be used in the finite strain regime.
KW - Anisotropic material
KW - Constraints
KW - Finite element analysis
KW - Mixed methods
UR - http://www.scopus.com/inward/record.url?scp=85036619142&partnerID=8YFLogxK
U2 - 10.1186/s40323-016-0079-3
DO - 10.1186/s40323-016-0079-3
M3 - Article
AN - SCOPUS:85036619142
VL - 3
JO - Advanced Modeling and Simulation in Engineering Sciences
JF - Advanced Modeling and Simulation in Engineering Sciences
IS - 1
M1 - 25
ER -