Stabilization-free virtual element method for 2D elastoplastic problems

authored by: Bing Bing Xu, Yi Fan Wang, Peter Wriggers
Abstract: In this paper, a novel first- and second-order stabilization-free virtual element method is proposed for two-dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more reliable. The main idea is to modify the virtual element space to allow the computation of the higher-order (Formula presented.) projection operator, ensuring that the strain and stress represent the element energy accurately. Considering the flexibility of the stabilization-free virtual element method, the elastoplastic mechanical problems can be solved by radial return methods known from the traditional finite element framework. (Formula presented.) plasticity with hardening is considered for modeling the nonlinear response. Several numerical examples are provided to illustrate the capability and accuracy of the stabilization-free virtual element method.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Dalian University of Technology
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 125
No. of pages: 22
ISSN: 0029-5981
Publication date: 19.07.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, Engineering(all), Applied Mathematics
Electronic version(s): https://doi.org/10.1002/nme.7490 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{22943ed6d1bd4f07b4adb81851fef05f,
title = "Stabilization-free virtual element method for 2D elastoplastic problems",
abstract = "In this paper, a novel first- and second-order stabilization-free virtual element method is proposed for two-dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more reliable. The main idea is to modify the virtual element space to allow the computation of the higher-order (Formula presented.) projection operator, ensuring that the strain and stress represent the element energy accurately. Considering the flexibility of the stabilization-free virtual element method, the elastoplastic mechanical problems can be solved by radial return methods known from the traditional finite element framework. (Formula presented.) plasticity with hardening is considered for modeling the nonlinear response. Several numerical examples are provided to illustrate the capability and accuracy of the stabilization-free virtual element method.",
keywords = "nonlinear, plasticity, stabilization-free, virtual element method",
author = "Xu, {Bing Bing} and Wang, {Yi Fan} and Peter Wriggers",
note = "Publisher Copyright: {\textcopyright} 2024 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.",
year = "2024",
month = jul,
day = "19",
doi = "10.1002/nme.7490",
language = "English",
volume = "125",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "15",
}