# On the impossibility of arbitrary deformations in nonlinear elasticity

On the impossibility of arbitrary deformations in nonlinear elasticity We employ partly Sobolev classes to obtain a necessary condition for mappings of $$W^{1,p}$$ W 1 , p -class to be deformations of nonlinearly elastic bodies that can be induced by $$L^{q}$$ L q -forces, $$1\le p,\,q <\infty$$ 1 ≤ p , q < ∞ . This condition is useful for studying continuous deformations of non-homogeneous materials and for obtaining stable numerical methods for nonlinear elasticity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

# On the impossibility of arbitrary deformations in nonlinear elasticity

, Volume 69 (1) – Nov 29, 2017
8 pages

/lp/springer_journal/on-the-impossibility-of-arbitrary-deformations-in-nonlinear-elasticity-M6ZDdkFSsn
Publisher
Springer Journals
Copyright © 2017 by Springer International Publishing AG, part of Springer Nature
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0895-4
Publisher site
See Article on Publisher Site

### Abstract

We employ partly Sobolev classes to obtain a necessary condition for mappings of $$W^{1,p}$$ W 1 , p -class to be deformations of nonlinearly elastic bodies that can be induced by $$L^{q}$$ L q -forces, $$1\le p,\,q <\infty$$ 1 ≤ p , q < ∞ . This condition is useful for studying continuous deformations of non-homogeneous materials and for obtaining stable numerical methods for nonlinear elasticity.

### Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Nov 29, 2017

## 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
that matters to you.

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. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations