Interaction of Elastic Waves in an Isotropic Solid

Nonlinear elasticity theory is used to investigate the scattering of two intersecting, plane, elastic waves in a homogeneous, isotropic medium. A criterion for the occurrence of a strong scattered wave is derived. The criterion is formulated as a relationship between the first-order elastic constants of the material, the angle between the intersecting wave vectors, and the ratio of wave frequencies. The exact formulation also depends on the type of intersecting waves, i.e., longitudinal or transverse. The amplitude of the scattered wave is found to be proportional to the volume of interaction and dependent on the third-order elastic constants of the material. Numerical results are given for wave scattering polystyrene.