Finite element formulations for large strain anisotropic material with inextensible fibers

authored by: P. Wriggers, J. Schröder, F. Auricchio
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.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Duisburg-Essen
University of Pavia
Type: Article
Journal: Advanced Modeling and Simulation in Engineering Sciences
Volume: 3
Publication date: 11.08.2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Engineering (miscellaneous), Computer Science Applications, Applied Mathematics
Electronic version(s): https://doi.org/10.1186/s40323-016-0079-3 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{cf2ad88b274141c3a5c9492cdb01fb54,
title = "Finite element formulations for large strain anisotropic material with inextensible fibers",
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",
author = "P. Wriggers and J. Schr{\"o}der and F. Auricchio",
note = "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.",
year = "2016",
month = aug,
day = "11",
doi = "10.1186/s40323-016-0079-3",
language = "English",
volume = "3",
journal = "Advanced Modeling and Simulation in Engineering Sciences",
issn = "2213-7467",
publisher = "Springer Open",
number = "1",
}