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Published January 2010 | public
Journal Article

On Maximally Dissipative Shock Waves in Nonlinear Elasticity

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.

Additional Information

© 2010 Springer. Received: 4 August 2009; accepted: 22 August 2009; published online: 17 September 2009.

Additional details

Created:
August 21, 2023
Modified:
October 19, 2023