Response of a nonlinear elastic general Cosserat brick element in simulations typically exhibiting locking and hourglassing

authored by: Stefan Loehnert, E. F.I. Boerner, M. B. Rubin, Peter Wriggers
Abstract: A comparison between the recently developed Cosserat brick element (see [9]) and other standard elements known from the literature is presented in this paper. The Cosserat brick element uses a director vector formulation based on the theory of a Cosserat point. The strain energy for a hyperelastic element is split additively into parts for homogeneous and inhomogeneous deformations respectively. The kinetic response due to inhomogeneous deformations uses constitutive constants that are determined by analytical solutions of a rectangular parallelepiped to the deformation modes of bending, torsion and hourglassing. Standard tests are performed which typically exhibit hourglassing or locking for many other finite elements. These tests include problems for beam and plate bending, shell structures and nearly incompressible materials, as well as for buckling under high pressure loads. For all these critical tests the Cosserat brick element exhibits robustness and reliability. Moreover, it does not depend on user-tuned stabilization parameters. Thus, it shows promise of being a truly user-friendly element for problems in nonlinear elasticity.
Organisation(s): Institute of Mechanics and Computational Mechanics
External Organisation(s): Technion-Israel Institute of Technology
Type: Article
Journal: Computational mechanics
Volume: 36
Pages: 255-265
No. of pages: 11
ISSN: 0178-7675
Publication date: 2005
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-005-0662-9 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{f5976c608a604cfb9158a41d105234c7,
title = "Response of a nonlinear elastic general Cosserat brick element in simulations typically exhibiting locking and hourglassing",
abstract = "A comparison between the recently developed Cosserat brick element (see [9]) and other standard elements known from the literature is presented in this paper. The Cosserat brick element uses a director vector formulation based on the theory of a Cosserat point. The strain energy for a hyperelastic element is split additively into parts for homogeneous and inhomogeneous deformations respectively. The kinetic response due to inhomogeneous deformations uses constitutive constants that are determined by analytical solutions of a rectangular parallelepiped to the deformation modes of bending, torsion and hourglassing. Standard tests are performed which typically exhibit hourglassing or locking for many other finite elements. These tests include problems for beam and plate bending, shell structures and nearly incompressible materials, as well as for buckling under high pressure loads. For all these critical tests the Cosserat brick element exhibits robustness and reliability. Moreover, it does not depend on user-tuned stabilization parameters. Thus, it shows promise of being a truly user-friendly element for problems in nonlinear elasticity.",
keywords = "Cosserat Theory, Finite Elasticity, Finite Element Technology, Hourglassing, Locking, Nearly Incompressible",
author = "Stefan Loehnert and Boerner, {E. F.I.} and Rubin, {M. B.} and Peter Wriggers",
year = "2005",
doi = "10.1007/s00466-005-0662-9",
language = "English",
volume = "36",
pages = "255--265",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "4",
}