Isogeometric contact

A review

authored by: Laura De Lorenzis, Peter Wriggers, Thomas J.R. Hughes
Abstract: This paper reviews the currently available computational contact formulations within the framework of isogeometric analysis (IGA). As opposed to conventional Lagrange discretizations, IGA basis functions feature higher and tailorable inter-element continuity, which translates into evident advantages for the description of interacting surfaces, especially in presence of large displacements and large sliding. This has recently motivated the proposal of several isogeometric contact treatments, based on different ways to incorporate the contact contribution into the variational form of a continuum mechanics problem and to formulate its discretized version. After a brief overview of conventional and isogeometric basis functions as well as conventional contact mechanics approaches, the available isogeometric contact formulations are examined. Attention is paid to the favorable and unfavorable features they share with their finite element counterparts, as well as to the consequences stemming from the use of IGA basis functions. The main needs for future research emerging from the current state of the art are outlined.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Technische Universität Braunschweig
University of Texas at Austin
Type: Review article
Journal: GAMM Mitteilungen
Volume: 37
Pages: 85-123
No. of pages: 39
ISSN: 0936-7195
Publication date: 07.07.2014
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Materials Science, General Physics and Astronomy, Applied Mathematics
Electronic version(s): https://doi.org/10.1002/gamm.201410005 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{28d8c42bd91b4f3588f3df01cb7bd895,
title = "Isogeometric contact: A review",
abstract = "This paper reviews the currently available computational contact formulations within the framework of isogeometric analysis (IGA). As opposed to conventional Lagrange discretizations, IGA basis functions feature higher and tailorable inter-element continuity, which translates into evident advantages for the description of interacting surfaces, especially in presence of large displacements and large sliding. This has recently motivated the proposal of several isogeometric contact treatments, based on different ways to incorporate the contact contribution into the variational form of a continuum mechanics problem and to formulate its discretized version. After a brief overview of conventional and isogeometric basis functions as well as conventional contact mechanics approaches, the available isogeometric contact formulations are examined. Attention is paid to the favorable and unfavorable features they share with their finite element counterparts, as well as to the consequences stemming from the use of IGA basis functions. The main needs for future research emerging from the current state of the art are outlined.",
keywords = "contact mechanics, interface modeling, isogeometric analysis, NURBS, smoothing, state of the art review",
author = "{De Lorenzis}, Laura and Peter Wriggers and Hughes, {Thomas J.R.}",
year = "2014",
month = jul,
day = "7",
doi = "10.1002/gamm.201410005",
language = "English",
volume = "37",
pages = "85--123",
journal = "GAMM Mitteilungen",
issn = "0936-7195",
publisher = "Wiley-VCH Verlag",
number = "1",
}