Acoustic nonlinearity parameters in hyperelastic solids with quadratic nonlinearity

In general, the nonlinear behavior of an elastic wave in isotropic hyperelastic solids with quadratic nonlinearity depends on five independent elastic constants, namely, the three third-order elastic constants and two second-order elastic constants. In this article, we show that such nonlinear behavior can be described fully by only three independent non-dimensional parameters if the wave motion is two-dimensional. Furthermore, if the motion is a plane wave, only two independent non-dimensional parameters are needed to fully describe the nonlinear behavior of the wave. These results are useful for conducting numerical simulations and for interpreting experimental measurement data.