Details
| Original language | English |
|---|---|
| Title of host publication | Multiscale Modeling of Heterogeneous Structures |
| Editors | Peter Wriggers, Olivier Allix, Jurica Soric |
| Publisher | Springer Verlag |
| Pages | 205-231 |
| Number of pages | 27 |
| ISBN (Print) | 9783319654621 |
| Publication status | Published - 2 Dec 2017 |
| Event | International Workshop on Multiscale Modeling of Heterogeneous Structures, MUMO 2016 - Dubrovnik, Croatia Duration: 21 Sept 2016 → 23 Sept 2016 |
Publication series
| Name | Lecture Notes in Applied and Computational Mechanics |
|---|---|
| Volume | 86 |
| ISSN (Print) | 1613-7736 |
Abstract
Anisotropic material with inextensive or nearly inextensible fibers introduce constraints in the mathematical formulations of the underlying differential equations from mechanics. 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 schemes like the finite element method or the virtual 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 for finite elements and virtual elements that can handle anisotropic materials with inextensive and nearly inextensive fibers. 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, Virtual element schemes
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
Cite this
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Multiscale Modeling of Heterogeneous Structures. ed. / Peter Wriggers; Olivier Allix; Jurica Soric. Springer Verlag, 2017. p. 205-231 (Lecture Notes in Applied and Computational Mechanics; Vol. 86).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Finite and Virtual Element Formulations for Large Strain Anisotropic Material with Inextensive Fibers
AU - Wriggers, P.
AU - Hudobivnik, B.
AU - Schröder, J.
N1 - Funding information: The first and third author acknowledge the support of the “Deutsche Forschungsgemeinschaft” under contract of the Priority Program 1748 ‘Reliable simulation techniques in solid mechanics: Development of non-standard discretization methods, mechanical and mathematical analysis’ under the project WR 19/50-1 and SCHR 570/23-1.
PY - 2017/12/2
Y1 - 2017/12/2
N2 - Anisotropic material with inextensive or nearly inextensible fibers introduce constraints in the mathematical formulations of the underlying differential equations from mechanics. 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 schemes like the finite element method or the virtual 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 for finite elements and virtual elements that can handle anisotropic materials with inextensive and nearly inextensive fibers. 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 inextensive or nearly inextensible fibers introduce constraints in the mathematical formulations of the underlying differential equations from mechanics. 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 schemes like the finite element method or the virtual 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 for finite elements and virtual elements that can handle anisotropic materials with inextensive and nearly inextensive fibers. 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
KW - Virtual element schemes
UR - http://www.scopus.com/inward/record.url?scp=85037853207&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-65463-8_11
DO - 10.1007/978-3-319-65463-8_11
M3 - Conference contribution
AN - SCOPUS:85037853207
SN - 9783319654621
T3 - Lecture Notes in Applied and Computational Mechanics
SP - 205
EP - 231
BT - Multiscale Modeling of Heterogeneous Structures
A2 - Wriggers, Peter
A2 - Allix, Olivier
A2 - Soric, Jurica
PB - Springer Verlag
T2 - International Workshop on Multiscale Modeling of Heterogeneous Structures, MUMO 2016
Y2 - 21 September 2016 through 23 September 2016
ER -