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REVIEW ARTICLES: General Lectures

Nonlinear Hyperbolic Waves in Hyperelastic Solids

[+] Author and Article Information
J. B. Haddow

Department of Mechanical Engineering, University of Victoria, PO Box 3055, Victoria, BC, Canada V8W 3P6

Appl. Mech. Rev 46(12), 527-539 (Dec 01, 1993) (13 pages) doi:10.1115/1.3120314 History: Online April 29, 2009

Abstract

This paper considers hyperbolic, one spatial dimension nonlinear wave propagation in a hyperelastic solid, and a discussion of the basic theory is presented. Constitutive relations for compressible rubberlike materials, whose internal energies can be expressed as the sum of a function of specific volume only and a function of temperature only, are discussed. These relations are assumed for the analysis of a class of plane wave problems and similarity solutions are obtained. Thermal effects, including the effect of the jump in entropy across a shock for a problem of uncoupled longitudinal wave propagation, are taken into account, however heat conduction is neglected. Solutions for a piezotropic model, which is a model for which mechanical and thermal effects are uncoupled, are obtained for comparison purposes. An axisymmetric problem is also discussed.

Copyright © 1993 by American Society of Mechanical Engineers
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