A stabilization technique to avoid hourglassing in finite elasticity

authored by: S. Reese, Peter Wriggers
Abstract: Enhanced strain element formulations are known to show an outstanding performance in many applications. The stability of these elements, however, cannot be guaranteed for general deformation states and arbitrarily shaped elements. In order to overcome this deficiency, we develop an innovative control technique based on a modal analysis on element level. The control is completely automatic in the sense that no artificial factors are introduced. The computational effort is negligible. The key to the approach is the split of the element tangent matrix into constant and hourglass parts which is not possible for the classical enhanced strain concept in general. This motivates the use of a recently developed reduced integration method, which, since its stabilization part is derived on the basis of the enhanced strain method, shows the same performance and retains the crucial split. Using this formulation in combination with the new control technique, leads to a 'smart' element which is free of hourglass instabilities and generally applicable, also for strongly distorted meshes.
Organisation(s): Institute of Mechanics and Computational Mechanics
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 48
Pages: 79-109
No. of pages: 31
ISSN: 0029-5981
Publication date: 23.03.2000
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, General Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1002/(SICI)1097-0207(20000510)48:1<79::AID-NME869>3.0.CO;2-D (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{00916cfbeb0043759c8dbc9e0414d83a,
title = "A stabilization technique to avoid hourglassing in finite elasticity",
abstract = "Enhanced strain element formulations are known to show an outstanding performance in many applications. The stability of these elements, however, cannot be guaranteed for general deformation states and arbitrarily shaped elements. In order to overcome this deficiency, we develop an innovative control technique based on a modal analysis on element level. The control is completely automatic in the sense that no artificial factors are introduced. The computational effort is negligible. The key to the approach is the split of the element tangent matrix into constant and hourglass parts which is not possible for the classical enhanced strain concept in general. This motivates the use of a recently developed reduced integration method, which, since its stabilization part is derived on the basis of the enhanced strain method, shows the same performance and retains the crucial split. Using this formulation in combination with the new control technique, leads to a 'smart' element which is free of hourglass instabilities and generally applicable, also for strongly distorted meshes.",
keywords = "Distorted meshes, Enhanced strain method, Hourglass stabilization, One Gauss point integration, Plane strain state, Smart elements",
author = "S. Reese and Peter Wriggers",
year = "2000",
month = mar,
day = "23",
doi = "10.1002/(SICI)1097-0207(20000510)48:1<79::AID-NME869>3.0.CO;2-D",
language = "English",
volume = "48",
pages = "79--109",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "1",
}