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On the dissipation associated with equilibrium shocks in finite elasticity

Knowles, James K. (1979) On the dissipation associated with equilibrium shocks in finite elasticity. Journal of Elasticity, 9 (2). pp. 131-158. ISSN 0374-3535. doi:10.1007/BF00041322.

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Equilibrium fields with discontinuous displacement gradients can occur in finite elasticity for certain materials. The presence of such “equilibrium shocks” affects the energy balance in the elastostatic field, and the present paper is concerned with a notion of dissipation associated with this energy balance. A dissipation inequality is proposed for three-dimensional equilibrium shocks for both compressible and incompressible materials. The consequences of this inequality are studied for weak shocks in plane strain for compressible materials and for shocks of arbitrary strength in anti-plane strain for a class of incompressible materials. A thermodynamic argument for the dissipation inequality is also given.

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Additional Information:© 1979 Sijthoff & Noordhoff International Publishers. Received March 20. 1978. The results communicated in this paper were obtained in the course of an investigation supported by Contract N00014-75-C-0196 between the California Institute of Technology and the Office of Naval Research. The author gratefully acknowledges helpful discussions with Eli Sternberg as well as the contribution of James Rice in connection with the material of the final section.
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Office of Naval Research (ONR)N00014-75-C-0196
Issue or Number:2
Record Number:CaltechAUTHORS:20151109-153157919
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ID Code:62011
Deposited On:09 Nov 2015 23:51
Last Modified:10 Nov 2021 22:56

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