Efficient virtual element formulations for compressible and incompressible finite deformations

Efficient virtual element formulations for compressible and incompressible finite deformations 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 compressible and incompressible nonlinear elasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered: for these, the ansatz functions are linear along element edges. The various formulations considered are based on minimization of energy, with a novel construction of the stabilization energy. The formulations are investigated through a series of numerical examples, which demonstrate their efficiency, convergence properties, and for the case of nearly incompressible and incompressible materials, locking-free behaviour. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Mechanics Springer Journals

Efficient virtual element formulations for compressible and incompressible finite deformations

Loading next page...
 
/lp/springer_journal/efficient-virtual-element-formulations-for-compressible-and-x4peu0pb7r
Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Theoretical and Applied Mechanics; Computational Science and Engineering; Classical and Continuum Physics
ISSN
0178-7675
eISSN
1432-0924
D.O.I.
10.1007/s00466-017-1405-4
Publisher site
See Article on Publisher Site

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 compressible and incompressible nonlinear elasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered: for these, the ansatz functions are linear along element edges. The various formulations considered are based on minimization of energy, with a novel construction of the stabilization energy. The formulations are investigated through a series of numerical examples, which demonstrate their efficiency, convergence properties, and for the case of nearly incompressible and incompressible materials, locking-free behaviour.

Journal

Computational MechanicsSpringer Journals

Published: Apr 6, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off