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On Maximally Dissipative Shock Waves in Nonlinear Elasticity

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Abstract

Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according to a definite kinetic relation, which we characterize and illustrate with examples.

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  1. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, 91125, USA

    James K. Knowles

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  1. James K. Knowles
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Correspondence to James K. Knowles.

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Knowles, J.K. On Maximally Dissipative Shock Waves in Nonlinear Elasticity. J Elasticity 98, 13–23 (2010). https://doi.org/10.1007/s10659-009-9221-5

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  • DOI: https://doi.org/10.1007/s10659-009-9221-5

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