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Stabilization-free virtual element method for 3D hyperelastic problems.

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Title: Stabilization-free virtual element method for 3D hyperelastic problems.
Authors: Xu, Bing-Bing1 (AUTHOR) bingbing.xu@ikm.uni-hannover.de, Peng, Fan2 (AUTHOR) pengfan33@chd.edu.cn, Wriggers, Peter1 (AUTHOR) wriggers@ikm.uni-hannover.de
Source: Computational Mechanics. Jun2025, Vol. 75 Issue 6, p1687-1701. 15p.
Subjects: Nonlinear equations, Graphical projection, Elastoplasticity, Elasticity
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 L 2 projection of the gradient. This paper reviews the calculation process of the traditional H 1 projection operator; and describes in detail how to calculate the high-order L 2 projection operator for three-dimensional problems. Based on this high-order L 2 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. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Stabilization-free virtual element method for 3D hyperelastic problems.
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  Data: 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 L 2 projection of the gradient. This paper reviews the calculation process of the traditional H 1 projection operator; and describes in detail how to calculate the high-order L 2 projection operator for three-dimensional problems. Based on this high-order L 2 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00466-024-02501-4
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      – Code: eng
        Text: English
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        StartPage: 1687
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        Type: general
      – SubjectFull: Graphical projection
        Type: general
      – SubjectFull: Elastoplasticity
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      – SubjectFull: Elasticity
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              M: 06
              Text: Jun2025
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              Y: 2025
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