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Impact-induced tensile waves in a rubberlike material

Knowles, James K. (2002) Impact-induced tensile waves in a rubberlike material. SIAM Journal on Applied Mathematics, 62 (4). pp. 1153-1175. ISSN 0036-1399. http://resolver.caltech.edu/CaltechAUTHORS:KNOsiamjam02

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Abstract

This paper concerns the propagation of impact-generated tensile waves in a one-dimensional bar made of a rubberlike material. Because the stress-strain curve changes from concave to convex as the strain increases, the governing quasi-linear system of partial differential equations, though hyperbolic, fails to be genuinely nonlinear so that the standard form of the boundary-initial value problem corresponding to impact is not well-posed at all levels of loading. When the problem fails to be well-posed, it does so by exhibiting a massive loss of uniqueness, even though an entropy-like dissipation inequality is in force. Because the breakdown in uniqueness is reminiscent of a similar phenomenon that occurs in continuum-mechanical models for impact-induced phase transitions, a mathematically suitable, though physically unmotivated, supplementary selection mechanism for determining the solution naturally suggests itself. We describe in detail the solutions determined by two special forms of this selection mechanism, and we show that these two solutions provide bounds on the impact response, regardless of the selection principle used.


Item Type:Article
Additional Information:© 2002 Society for Industrial and Applied Mathematics. Received by the editors April 18, 2001; accepted for publication (in revised form) October 21, 2001; published electronically April 3, 2002. I am indebted to a referee for calling the paper [12] by Schulze and Shearer to my attention.
Subject Keywords:rubber, impact, genuine nonlinearity, kinetic relations, propagating phase boundaries, conservation-laws, nonclassical shocks, solids, transitions
Record Number:CaltechAUTHORS:KNOsiamjam02
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KNOsiamjam02
Alternative URL:http://dx.doi.org/10.1137/S0036139901388234
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:853
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Oct 2005
Last Modified:26 Dec 2012 08:41

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