A low order virtual element formulation for finite elasto-plastic deformations

authored by: P. Wriggers, B. Hudobivnik
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 finite strain plasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered. The formulation is based on minimization of an incremental energy expression, with a novel construction of the stabilization energy for elasto-plasticity. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 327
Pages: 459-477
No. of pages: 19
ISSN: 0045-7825
Publication date: 13.10.2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2017.08.053 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{622fd9d5b8784c7a88a2f377e1f98412,
title = "A low order virtual element formulation for finite elasto-plastic deformations",
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 finite strain plasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered. The formulation is based on minimization of an incremental energy expression, with a novel construction of the stabilization energy for elasto-plasticity. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties.",
keywords = "Finite strain plasticity, Stabilization, VEM, Virtual element method",
author = "P. Wriggers and B. Hudobivnik",
note = "Funding information: The first author gratefully acknowledges support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 {\textquoteleft}Reliable simulation techniques in solid mechanics: Development of non- standard discretization methods, mechanical and mathematical analysis{\textquoteright} under the project WR 19/50-1.",
year = "2017",
month = oct,
day = "13",
doi = "10.1016/j.cma.2017.08.053",
language = "English",
volume = "327",
pages = "459--477",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}