Details
| Original language | English |
|---|---|
| Pages (from-to) | 255-265 |
| Number of pages | 11 |
| Journal | Computational mechanics |
| Volume | 36 |
| Issue number | 4 |
| Publication status | Published - 2005 |
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
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 36, No. 4, 2005, p. 255-265.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Response of a nonlinear elastic general Cosserat brick element in simulations typically exhibiting locking and hourglassing
AU - Loehnert, Stefan
AU - Boerner, E. F.I.
AU - Rubin, M. B.
AU - Wriggers, Peter
PY - 2005
Y1 - 2005
N2 - 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.
AB - 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.
KW - Cosserat Theory
KW - Finite Elasticity
KW - Finite Element Technology
KW - Hourglassing
KW - Locking
KW - Nearly Incompressible
UR - http://www.scopus.com/inward/record.url?scp=23744488297&partnerID=8YFLogxK
U2 - 10.1007/s00466-005-0662-9
DO - 10.1007/s00466-005-0662-9
M3 - Article
AN - SCOPUS:23744488297
VL - 36
SP - 255
EP - 265
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 4
ER -