0
REVIEW ARTICLES

Nonlinear Waves in Nonlocal Media

[+] Author and Article Information
J. Engelbrecht

Institute of Cybernetics and Estonian Academy of Sciences, Kohtu 6, EE-0001 Tallinn, Estonia

M. Braun

Gerhard-Mercator-Universität Duisburg, Fachgebiet Mechanik, D-47048 Duisburg, Germany

Appl. Mech. Rev 51(8), 475-488 (Aug 01, 1998) (14 pages) doi:10.1115/1.3099016 History: Online April 20, 2009

Abstract

This review article gives a brief overview on nonlocal theories in solid mechanics from the viewpoint of wave motion. The influence of two essential qualities of solids—nonlocality and nonlinearity—is discussed. The effects of microstructure are analyzed in order to understand their role in nonlocal theories. The various models are specified on the level of one-dimensional unidirectional motion in order to achieve mathematical clarity of interpreting physical phenomena. Three main types of evolution equations are shown to govern deformation waves under such assumptions. Based on the dispersion analysis, weak, true, and strong nonlocalities are distinguished. There are 75 references included with this article.

Copyright © 1998 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In