Details
| Original language | English |
|---|---|
| Pages (from-to) | 407-416 |
| Number of pages | 10 |
| Journal | Computational mechanics |
| Volume | 42 |
| Issue number | 3 |
| Publication status | Published - 7 Mar 2008 |
Abstract
A three-dimensional 8-node brick continuum finite element formulation for incompressible finite elasticity is presented. The core idea is to introduce a substructure consisting of eight sub-elements inside each finite element, further referred to as macro-element. For each of the sub-elements, the deformation is averaged. The weak form for each sub-element is based on the Hu-Washizu principle. The response of each sub-element is assembled and projected onto the eight external nodes of the macro-element. The introduction of deformable sub-elements in case of incompressible elasticity has two major advantages. Firstly, it is possible to suppress locking by evaluating the volumetric part of the response only in the macro-element instead of in each of the sub-elements. Secondly, no integration is necessary due to the use of averaged deformations on the sub-element level. The idea originates from the Cosserat point element developed in Nadler and Rubin (Int J Solids Struct 40:4585-4614, 2003). A consistent transition between the Cosserat point macro-element and a displacement macro-element formulation using a kinematical description from the enhanced strain element formulation (Flanagan, Belytschko in Int J Numer Methods Eng 17:679-706, 1981) or (Belytschko et al. in Comput Methods Appl Mech Eng 43:251-276, 1984) and the principle of Hu-Washizu is presented. The performance is examined by means of numerical examples.
Keywords
- Finite elasticity, Finite element technology, Incompressibility
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. 42, No. 3, 07.03.2008, p. 407-416.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A macro-element for incompressible finite deformations based on a volume averaged deformation gradient
AU - Boerner, E. F.I.
AU - Wriggers, Peter
PY - 2008/3/7
Y1 - 2008/3/7
N2 - A three-dimensional 8-node brick continuum finite element formulation for incompressible finite elasticity is presented. The core idea is to introduce a substructure consisting of eight sub-elements inside each finite element, further referred to as macro-element. For each of the sub-elements, the deformation is averaged. The weak form for each sub-element is based on the Hu-Washizu principle. The response of each sub-element is assembled and projected onto the eight external nodes of the macro-element. The introduction of deformable sub-elements in case of incompressible elasticity has two major advantages. Firstly, it is possible to suppress locking by evaluating the volumetric part of the response only in the macro-element instead of in each of the sub-elements. Secondly, no integration is necessary due to the use of averaged deformations on the sub-element level. The idea originates from the Cosserat point element developed in Nadler and Rubin (Int J Solids Struct 40:4585-4614, 2003). A consistent transition between the Cosserat point macro-element and a displacement macro-element formulation using a kinematical description from the enhanced strain element formulation (Flanagan, Belytschko in Int J Numer Methods Eng 17:679-706, 1981) or (Belytschko et al. in Comput Methods Appl Mech Eng 43:251-276, 1984) and the principle of Hu-Washizu is presented. The performance is examined by means of numerical examples.
AB - A three-dimensional 8-node brick continuum finite element formulation for incompressible finite elasticity is presented. The core idea is to introduce a substructure consisting of eight sub-elements inside each finite element, further referred to as macro-element. For each of the sub-elements, the deformation is averaged. The weak form for each sub-element is based on the Hu-Washizu principle. The response of each sub-element is assembled and projected onto the eight external nodes of the macro-element. The introduction of deformable sub-elements in case of incompressible elasticity has two major advantages. Firstly, it is possible to suppress locking by evaluating the volumetric part of the response only in the macro-element instead of in each of the sub-elements. Secondly, no integration is necessary due to the use of averaged deformations on the sub-element level. The idea originates from the Cosserat point element developed in Nadler and Rubin (Int J Solids Struct 40:4585-4614, 2003). A consistent transition between the Cosserat point macro-element and a displacement macro-element formulation using a kinematical description from the enhanced strain element formulation (Flanagan, Belytschko in Int J Numer Methods Eng 17:679-706, 1981) or (Belytschko et al. in Comput Methods Appl Mech Eng 43:251-276, 1984) and the principle of Hu-Washizu is presented. The performance is examined by means of numerical examples.
KW - Finite elasticity
KW - Finite element technology
KW - Incompressibility
UR - http://www.scopus.com/inward/record.url?scp=44449156711&partnerID=8YFLogxK
U2 - 10.1007/s00466-008-0250-x
DO - 10.1007/s00466-008-0250-x
M3 - Article
AN - SCOPUS:44449156711
VL - 42
SP - 407
EP - 416
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 3
ER -