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RESEARCH PAPERS

Simple Waves and Shock Waves Generated by an Incident Shock Wave in Two-Dimensional Hyperelastic Materials

[+] Author and Article Information
Yongchi Li

Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui, China

T. C. T. Ting

Department of Civil Engineering, Mechanics and Metallurgy, University of Illinois at Chicago, Chicago, Ill. 60680

J. Appl. Mech 51(3), 586-594 (Sep 01, 1984) (9 pages) doi:10.1115/1.3167678 History: Received November 01, 1983; Revised January 01, 1984; Online July 21, 2009

Abstract

The reflection of an oblique plane shock wave from a boundary in a two-dimensional isotropic hyperelastic material is studied. For plane strain deformations, the strain energy function W is a function of two invariants p and q of the deformation gradient. There are, in general, two reflected waves each of which can be a simple wave or a shock wave. For a special class of materials for which the strain energy function W(p, q) represents a developable surface (of which harmonic materials are particular examples), one of the reflected waves is always a shock wave. It is shown that there are materials other than harmonic materials for which the wave speeds are independent of the direction of propagation. Illustrative examples are presented to show how one can determine the reflected waves from a rigid boundary. It is also shown that for certain incident shock waves, there exists only one reflected wave.

Copyright © 1984 by ASME
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