Finite-Amplitude Waves in Solids

The theoretical foundation for weakly nonlinear elastic waves in isotropic solids is developed. Lagrangian coordinates are used to obtain the equation of motion in terms of the Piola-Kirchhoff stress tensor, which is a function of the strain energy density. Notations employed for elastic constants in different expansions of the strain energy density are related to those introduced by Landau and Lifshitz. Use of the acoustoelastic effect to determine the third-order elastic constants is described. Solutions are presented for second-harmonic generation in a longitudinal plane wave. Finally, the nonlinear parabolic (KZK) equation for longitudinal elastic wave beams is derived.