Details
| Original language | English |
|---|---|
| Article number | 117258 |
| Number of pages | 22 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 431 |
| Early online date | 30 Jul 2024 |
| Publication status | Published - 1 Nov 2024 |
Abstract
In this work, we develop a general high-order virtual element method for three-dimensional linear and nonlinear elastic problems. Applications of the virtual element method (VEM) in three-dimensional mechanics include linear elasticity problems, finite elastic strain problems, finite deformation plasticity problems, etc. But besides linear elastic problems, see e.g. Visinoni, 2024, the numerical schemes were all based on a first-order approximation of the displacement. We derive three-dimensional elastic problems, including linear elastic problems and for the first time hyperelastic problems. Similar to previous work, we discuss the calculation method of three-dimensional high-order projection operators of vector fields and calculate the tangent stiffness matrix of elastic problems according to the variational scheme. Since traditional VEM requires the use of stabilization terms to ensure the correctness of the rank of the stiffness matrix, we give suggestions for the selection of stabilization terms for high-order virtual element methods in both linear and nonlinear elasticity. Finally, we illustrate the accuracy, convergence, and stability of the high-order VEM for elastic problems by means of some classic elastic and hyperelastic examples. In addition, we also apply the developed methodology to some complex and difficult problems which illustrate the adaptability of the method to engineering problems.
Keywords
- Hyperelasticity, Nonlinear, Virtual element method
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 431, 117258, 01.11.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - High-order 3D virtual element method for linear and nonlinear elasticity
AU - Xu, Bing Bing
AU - Fan, Wei Long
AU - Wriggers, Peter
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2024/11/1
Y1 - 2024/11/1
N2 - In this work, we develop a general high-order virtual element method for three-dimensional linear and nonlinear elastic problems. Applications of the virtual element method (VEM) in three-dimensional mechanics include linear elasticity problems, finite elastic strain problems, finite deformation plasticity problems, etc. But besides linear elastic problems, see e.g. Visinoni, 2024, the numerical schemes were all based on a first-order approximation of the displacement. We derive three-dimensional elastic problems, including linear elastic problems and for the first time hyperelastic problems. Similar to previous work, we discuss the calculation method of three-dimensional high-order projection operators of vector fields and calculate the tangent stiffness matrix of elastic problems according to the variational scheme. Since traditional VEM requires the use of stabilization terms to ensure the correctness of the rank of the stiffness matrix, we give suggestions for the selection of stabilization terms for high-order virtual element methods in both linear and nonlinear elasticity. Finally, we illustrate the accuracy, convergence, and stability of the high-order VEM for elastic problems by means of some classic elastic and hyperelastic examples. In addition, we also apply the developed methodology to some complex and difficult problems which illustrate the adaptability of the method to engineering problems.
AB - In this work, we develop a general high-order virtual element method for three-dimensional linear and nonlinear elastic problems. Applications of the virtual element method (VEM) in three-dimensional mechanics include linear elasticity problems, finite elastic strain problems, finite deformation plasticity problems, etc. But besides linear elastic problems, see e.g. Visinoni, 2024, the numerical schemes were all based on a first-order approximation of the displacement. We derive three-dimensional elastic problems, including linear elastic problems and for the first time hyperelastic problems. Similar to previous work, we discuss the calculation method of three-dimensional high-order projection operators of vector fields and calculate the tangent stiffness matrix of elastic problems according to the variational scheme. Since traditional VEM requires the use of stabilization terms to ensure the correctness of the rank of the stiffness matrix, we give suggestions for the selection of stabilization terms for high-order virtual element methods in both linear and nonlinear elasticity. Finally, we illustrate the accuracy, convergence, and stability of the high-order VEM for elastic problems by means of some classic elastic and hyperelastic examples. In addition, we also apply the developed methodology to some complex and difficult problems which illustrate the adaptability of the method to engineering problems.
KW - Hyperelasticity
KW - Nonlinear
KW - Virtual element method
UR - http://www.scopus.com/inward/record.url?scp=85199810549&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.117258
DO - 10.1016/j.cma.2024.117258
M3 - Article
AN - SCOPUS:85199810549
VL - 431
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 117258
ER -