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Evolution of Failure Mechanisms in Composite Shell Structures Using Different Models Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Finite and Virtual Element Formulations for Large Strain Anisotropic Material with Inextensive Fibers

Authors : P. Wriggers, B. Hudobivnik, J. Schröder

Published in: Multiscale Modeling of Heterogeneous Structures

Publisher: Springer International Publishing

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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.

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Footnotes
1
It is well known that ill-conditioning can occur when a large penalty parameter \(C_c\) is selected. Thus in reality the penalty formulation is only able to approximately enforce the constraint condition (8).
 
2
In the linear case both conditions, while being different, yield a linear dependence on the components of the displacement gradient. Thus there the choice of using the same ansatz function for the pressure (incompressibility) and the fiber stress (anisotropy) is justified.
 
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Metadata
Title
Finite and Virtual Element Formulations for Large Strain Anisotropic Material with Inextensive Fibers
Authors
P. Wriggers
B. Hudobivnik
J. Schröder
Copyright Year
2018
Book
Multiscale Modeling of Heterogeneous Structures

Print ISBN: 978-3-319-65462-1

Electronic ISBN: 978-3-319-65463-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-65463-8_11

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