A Taylor–Hood type virtual element formulations for large incompressible strains

authored by: P. Wriggers, M. L. De Bellis, B. Hudobivnik
Abstract: Considerable progress has been made during the last decade with respect to the development of discretization techniques that are based on the virtual element method. Here we construct a new scheme for large strain problems that include incompressible material behavior. The idea is to use a formulations analogous to the classical Taylor–Hood element, Taylor and Hood (1972) which is based on a mixed principle where different interpolation functions are used for the deformation and pressure field. In this paper, a quadratic serendipity ansatz for the displacements is combined with a linear pressure field which leads to new virtual element formulations that are discussed and compared in this paper.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Chieti
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 385
ISSN: 0045-7825
Publication date: 01.11.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2021.114021 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{b16f19c4736b44c8b9f42652e45c9ec3,
title = "A Taylor–Hood type virtual element formulations for large incompressible strains",
abstract = "Considerable progress has been made during the last decade with respect to the development of discretization techniques that are based on the virtual element method. Here we construct a new scheme for large strain problems that include incompressible material behavior. The idea is to use a formulations analogous to the classical Taylor–Hood element, Taylor and Hood (1972) which is based on a mixed principle where different interpolation functions are used for the deformation and pressure field. In this paper, a quadratic serendipity ansatz for the displacements is combined with a linear pressure field which leads to new virtual element formulations that are discussed and compared in this paper.",
keywords = "Incompressibility, Large strains, Taylor Hood, Virtual element method",
author = "P. Wriggers and {De Bellis}, {M. L.} and B. Hudobivnik",
note = "Funding Information: The first author gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the collaborative research center CRC 1153 “Tailored Forming” while the third author acknowledges support for this research by the Cluster of Exellence (EXC 2122) “PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines” . ",
year = "2021",
month = nov,
day = "1",
doi = "10.1016/j.cma.2021.114021",
language = "English",
volume = "385",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}