publication . Article . 2009

On Maximally Dissipative Shock Waves in Nonlinear Elasticity

Name: On Maximally Dissipative Shock Waves in Nonlinear Elasticity
Creator: James K. Knowles
Keywords: Mechanical Engineering, General Materials Science, Mechanics of Materials

James K. Knowles;

Open Access

Published: 17 Sep 2009

Publisher: Springer

Country: United States

Summary

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.

doi: 10.1007/s10659-009-9221-5

Subjects

free text keywords: Mechanical Engineering, General Materials Science, Mechanics of Materials, Mechanics, Elasticity (economics), Kinetic energy, Dissipation, Elastic solids, Classical mechanics, Physics, Nonlinear elasticity, Dissipative system, Shock wave

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