A modified Khokhlov-Zabolotskaya equation governing shear waves in a prestrained hyperelastic solid.
Weakly nonlinear, weakly diffracting, two-dimensional shear waves propagating in a prestrained hyperelastic solid are examined. A modification of the classical Khokhlov-Zabolotskaya equation is derived using a systematic perturbation scheme. Both dissipative and nondissipative materials were considered. The principal effect of the prestrain was seen to be the inclusion of a quadratic nonlinearity to the cubic nonlinearity found in the case of zero prestrain. Further new results include the shock jump relations and the prediction of shocks having a speed which is identical to the nonlinear wave speed ahead of or behind the shock. Explicit expressions for the nonlinearity coefficients for the special case of a Blatz-Ko material were provided.
Department of Engineering Science and Mechanics, Virginia Polytechnic Institute & State University, Blacksburg, Virginia 24061-0219, USA.
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Cramer
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Andrews