A low order 3D virtual element formulation for finite elasto–plastic deformations

verfasst von: Blaž Hudobivnik, Fadi Aldakheel, Peter Wriggers
Abstract: This work addresses an efficient low order 3D virtual element method for elastic–plastic solids undergoing large deformations. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The successful application of the method to non-linear problems such as finite strain elasticity and plasticity in 2D leads naturally to the question of its effectiveness and robustness in the third dimension. This work is concerned with the extensions of the virtual element method to problems of 3D finite strain plasticity. Low-order formulations for problems in three dimensions, with elements being arbitrary shaped polyhedra, are considered. The formulation is based on minimization of a pseudo energy expression, with a generalization of a stabilization techniques, introduced for two dimensional polygons, to the three-dimensional domain. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties. For comparison purposes, results of the standard finite element method are also demonstrated.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Typ: Artikel
Journal: Computational mechanics
Band: 63
Seiten: 253-269
Anzahl der Seiten: 17
ISSN: 0178-7675
Publikationsdatum: 15.02.2019
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Meerestechnik, Maschinenbau, Theoretische Informatik und Mathematik, Computational Mathematics, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.1007/s00466-018-1593-6 (Zugang: Geschlossen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{a7f0ab98ad954d4093a94f3aad018ef3,
title = "A low order 3D virtual element formulation for finite elasto–plastic deformations",
abstract = "This work addresses an efficient low order 3D virtual element method for elastic–plastic solids undergoing large deformations. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The successful application of the method to non-linear problems such as finite strain elasticity and plasticity in 2D leads naturally to the question of its effectiveness and robustness in the third dimension. This work is concerned with the extensions of the virtual element method to problems of 3D finite strain plasticity. Low-order formulations for problems in three dimensions, with elements being arbitrary shaped polyhedra, are considered. The formulation is based on minimization of a pseudo energy expression, with a generalization of a stabilization techniques, introduced for two dimensional polygons, to the three-dimensional domain. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties. For comparison purposes, results of the standard finite element method are also demonstrated.",
keywords = "Finite strain plasticity, Stabilization, Three-dimensional, Virtual element method VEM",
author = "Bla{\v z} Hudobivnik and Fadi Aldakheel and Peter Wriggers",
note = "Funding information: The corresponding author gratefully acknowledges support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable simulation techniques in solid mechanics: development of non-standard discretization methods, mechanical and mathematical analysis” under the project WR 19/50-1. The second author gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the Priority Program SPP 2020 under the project WR 19/58-1.",
year = "2019",
month = feb,
day = "15",
doi = "10.1007/s00466-018-1593-6",
language = "English",
volume = "63",
pages = "253--269",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "2",
}