Details
| Original language | English |
|---|---|
| Journal | Computational mechanics |
| Publication status | E-pub ahead of print - 27 May 2024 |
Abstract
In this work, we present a first-order stabilization-free virtual element method (SFVEM) for three-dimensional hyperelastic problems. Different from the conventional virtual element method, which necessitates additional stabilization terms in the bilinear formulation, the method developed in this work operates without the need for any stabilization. Consequently, it proves highly suitable for the computation of nonlinear problems. The stabilization-free virtual element method has been applied in two-dimensional hyperelasticity and three-dimensional elasticity problems. In this work, the format will be applied to three-dimensional hyperelasticity problems for the first time. Similar to the techniques used in the two-dimensional stabilization-free virtual element method, the new virtual element space is modified to allow the computation of the higher-order L2 projection of the gradient. This paper reviews the calculation process of the traditional H1 projection operator; and describes in detail how to calculate the high-order L2 projection operator for three-dimensional problems. Based on this high-order L2 projection operator, this paper extends the method to more complex three-dimensional nonlinear problems. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional hyperelastic problems.
Keywords
- Elastoplasticity, Nonlinear problems, Stabilization free, 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, 27.05.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stabilization-free virtual element method for 3D hyperelastic problems
AU - Xu, Bing Bing
AU - Peng, Fan
AU - Wriggers, Peter
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/5/27
Y1 - 2024/5/27
N2 - In this work, we present a first-order stabilization-free virtual element method (SFVEM) for three-dimensional hyperelastic problems. Different from the conventional virtual element method, which necessitates additional stabilization terms in the bilinear formulation, the method developed in this work operates without the need for any stabilization. Consequently, it proves highly suitable for the computation of nonlinear problems. The stabilization-free virtual element method has been applied in two-dimensional hyperelasticity and three-dimensional elasticity problems. In this work, the format will be applied to three-dimensional hyperelasticity problems for the first time. Similar to the techniques used in the two-dimensional stabilization-free virtual element method, the new virtual element space is modified to allow the computation of the higher-order L2 projection of the gradient. This paper reviews the calculation process of the traditional H1 projection operator; and describes in detail how to calculate the high-order L2 projection operator for three-dimensional problems. Based on this high-order L2 projection operator, this paper extends the method to more complex three-dimensional nonlinear problems. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional hyperelastic problems.
AB - In this work, we present a first-order stabilization-free virtual element method (SFVEM) for three-dimensional hyperelastic problems. Different from the conventional virtual element method, which necessitates additional stabilization terms in the bilinear formulation, the method developed in this work operates without the need for any stabilization. Consequently, it proves highly suitable for the computation of nonlinear problems. The stabilization-free virtual element method has been applied in two-dimensional hyperelasticity and three-dimensional elasticity problems. In this work, the format will be applied to three-dimensional hyperelasticity problems for the first time. Similar to the techniques used in the two-dimensional stabilization-free virtual element method, the new virtual element space is modified to allow the computation of the higher-order L2 projection of the gradient. This paper reviews the calculation process of the traditional H1 projection operator; and describes in detail how to calculate the high-order L2 projection operator for three-dimensional problems. Based on this high-order L2 projection operator, this paper extends the method to more complex three-dimensional nonlinear problems. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional hyperelastic problems.
KW - Elastoplasticity
KW - Nonlinear problems
KW - Stabilization free
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85194567139&partnerID=8YFLogxK
U2 - 10.1007/s00466-024-02501-4
DO - 10.1007/s00466-024-02501-4
M3 - Article
AN - SCOPUS:85194567139
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
ER -