Low-order locking-free mixed finite element formulation with approximation of the minors of the deformation gradient

authored by: Alex Kraus, Peter Wriggers, Nils Viebahn, Jörg Schröder
Abstract: In this work, a low-order mixed finite element formulation for three-dimensional nonlinear elastic problems is presented. The main goal of this paper is to develop a robust and efficient element formulation to overcome locking arising in the cases of hyperelastic bending, quasi-incompressibility, and anisotropy. For this, a low-order discretisation of a five-field Hu-Washizu functional written in terms of the minors of the Cauchy-Green tensor is used. For the tested boundary value problems, the proposed element formulation is more accurate and computational efficient than comparable element formulations.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Duisburg-Essen
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 120
Pages: 1011-1026
No. of pages: 16
ISSN: 0029-5981
Publication date: 10.07.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, General Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1002/nme.6168 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{3d618b0db91548e0a4ba9ece14ba8974,
title = "Low-order locking-free mixed finite element formulation with approximation of the minors of the deformation gradient",
abstract = "In this work, a low-order mixed finite element formulation for three-dimensional nonlinear elastic problems is presented. The main goal of this paper is to develop a robust and efficient element formulation to overcome locking arising in the cases of hyperelastic bending, quasi-incompressibility, and anisotropy. For this, a low-order discretisation of a five-field Hu-Washizu functional written in terms of the minors of the Cauchy-Green tensor is used. For the tested boundary value problems, the proposed element formulation is more accurate and computational efficient than comparable element formulations.",
keywords = "anisotropy, locking-free, mixed finite elements, nearly incompressible material",
author = "Alex Kraus and Peter Wriggers and Nils Viebahn and J{\"o}rg Schr{\"o}der",
note = "Funding information: The authors gratefully acknowledge the support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable Simulation Techniques in Solid Mechanics, Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis” for the project “Novel finite elements for anisotropic media at finite strain” (WR 19/50-1)(SCHR 570/23-1).",
year = "2019",
month = jul,
day = "10",
doi = "10.1002/nme.6168",
language = "English",
volume = "120",
pages = "1011--1026",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "8",
}