publication . Article . 2009

On Maximally Dissipative Shock Waves in Nonlinear Elasticity

James K. Knowles;
Open Access
  • Published: 17 Sep 2009
  • Publisher: Springer
  • Country: United States
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.
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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