A modified Khokhlov-Zabolotskaya equation governing shear waves in a prestrained hyperelastic solid

Abstract

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.