Details
| Original language | English |
|---|---|
| Pages (from-to) | 253-268 |
| Number of pages | 16 |
| Journal | Computational mechanics |
| Volume | 60 |
| Issue number | 2 |
| Publication status | Published - 6 Apr 2017 |
Abstract
The virtual element method has been developed over the last decade and applied to problems in elasticity and other areas. The successful application of the method to linear problems leads naturally to the question of its effectiveness in the nonlinear regime. This work is concerned with extensions of the virtual element method to problems of compressible and incompressible nonlinear elasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered: for these, the ansatz functions are linear along element edges. The various formulations considered are based on minimization of energy, with a novel construction of the stabilization energy. The formulations are investigated through a series of numerical examples, which demonstrate their efficiency, convergence properties, and for the case of nearly incompressible and incompressible materials, locking-free behaviour.
Keywords
- Mixed methods, Nonlinear elasticity, Stabilization, VEM, Virtual element method
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. 60, No. 2, 06.04.2017, p. 253-268.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Efficient virtual element formulations for compressible and incompressible finite deformations
AU - Wriggers, P.
AU - Reddy, B. D.
AU - Rust, W.
AU - Hudobivnik, B.
N1 - Funding information: The first author gratefully acknowledges support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 ‘Reliable simulation techniques in solid mechanics: Development of non- standard discretization methods, mechanical and mathematical analysis’ under the Project WR 19/50-1. The second author acknowledges the support of the National Research Foundation of South Africa, and the Alexander von Humboldt Foundation through a Georg Forster Research Fellowship.
PY - 2017/4/6
Y1 - 2017/4/6
N2 - The virtual element method has been developed over the last decade and applied to problems in elasticity and other areas. The successful application of the method to linear problems leads naturally to the question of its effectiveness in the nonlinear regime. This work is concerned with extensions of the virtual element method to problems of compressible and incompressible nonlinear elasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered: for these, the ansatz functions are linear along element edges. The various formulations considered are based on minimization of energy, with a novel construction of the stabilization energy. The formulations are investigated through a series of numerical examples, which demonstrate their efficiency, convergence properties, and for the case of nearly incompressible and incompressible materials, locking-free behaviour.
AB - The virtual element method has been developed over the last decade and applied to problems in elasticity and other areas. The successful application of the method to linear problems leads naturally to the question of its effectiveness in the nonlinear regime. This work is concerned with extensions of the virtual element method to problems of compressible and incompressible nonlinear elasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered: for these, the ansatz functions are linear along element edges. The various formulations considered are based on minimization of energy, with a novel construction of the stabilization energy. The formulations are investigated through a series of numerical examples, which demonstrate their efficiency, convergence properties, and for the case of nearly incompressible and incompressible materials, locking-free behaviour.
KW - Mixed methods
KW - Nonlinear elasticity
KW - Stabilization
KW - VEM
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85017174872&partnerID=8YFLogxK
U2 - 10.1007/s00466-017-1405-4
DO - 10.1007/s00466-017-1405-4
M3 - Article
AN - SCOPUS:85017174872
VL - 60
SP - 253
EP - 268
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 2
ER -