Computational Mechanics

, Volume 36, Issue 4, pp 255–265

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

  • S. Loehnert
  • E. F. I. Boerner
  • M. B. Rubin
  • P. Wriggers
Article

DOI: 10.1007/s00466-005-0662-9

Cite this article as:
Loehnert, S., Boerner, E., Rubin, M. et al. Comput Mech (2005) 36: 255. doi:10.1007/s00466-005-0662-9

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 TheoryFinite Element TechnologyFinite ElasticityHourglassingLockingNearly Incompressible

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • S. Loehnert
    • 1
  • E. F. I. Boerner
    • 1
  • M. B. Rubin
    • 2
  • P. Wriggers
    • 1
  1. 1.Institute of Mechanics and Computational MechanicsUniversity of HannoverHannoverGermany
  2. 2.Faculty of Mechanical EngineeringTechnion - Israel Institute of TechnologyHaifaIsrael