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The Quarterly Journal of Mechanics and Applied Mathematics 1969 22(3):261-281; doi:10.1093/qjmam/22.3.261
© 1969 by Oxford University Press
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ONE-DIMENSIONAL SHOCK WAVES AND ACCELERATION FRONTS IN NON-LINEAR VISCOELASTIC MATERIALS

ROBIN J. WATERSTON

( Department of Mathematics, University of Strathclyde Glasgow )

In this paper constitutive equations are derived for viscoelastic materials which are transversely isotropic or isotropic in their initial state, assuming that all displacements are small, but taking non-linear terms into account. We consider one-dimensional wave motion, and analyse the types of shock and acceleration front that can propagate. The results are displayed in such a way that they are readily comparable with the corresponding results for elastic materials, and it is found that close parallels exist. Conditions for the entropy to increase across each shock are obtained.


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