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


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
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