Fiber-reinforced materials

finite elements for the treatment of the inextensibility constraint

authored by: Ferdinando Auricchio, Giulia Scalet, Peter Wriggers
Abstract: The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Pavia
Type: Article
Journal: Computational mechanics
Volume: 60
Pages: 905-922
No. of pages: 18
ISSN: 0178-7675
Publication date: 20.07.2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-017-1437-9 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{3815d40194ca4086b5e0085ae4e85ada,
title = "Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint",
abstract = "The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.",
keywords = "Anisotropic material, Fiber-reinforced material, Finite element analysis, Inextensible fibers, Mixed finite element method",
author = "Ferdinando Auricchio and Giulia Scalet and Peter Wriggers",
year = "2017",
month = jul,
day = "20",
doi = "10.1007/s00466-017-1437-9",
language = "English",
volume = "60",
pages = "905--922",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "6",
}