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Dynamic cavitation with shocks in nonlinear elasticity

Published online by Cambridge University Press:  14 November 2011

K. A. Pericak-Spector  and
Scott J. Spector
K. A. Pericak-Spector
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901-4408, U.S.A
Scott J. Spector
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901-4408, U.S.A
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Abstract

The hyperbolic system of conservation laws that govern the motion of a homogeneous isotropic, nonlinearly elastic body is shown to have a discontinuous solution for a class of stored-energy functions of slow growth. This solution is admissible by the usual entropy criterion and is in fact preferred by the entropy-rate criterion over the smooth equilibrium solution to the same problem. The existence of such a dissipative solution shows that the equilibrium solution is dynamically unstable. This instability cannot be ascertained by linearisation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 4 , 1997 , pp. 837 - 857
Copyright
Copyright © Royal Society of Edinburgh 1997

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