Wave interaction coefficients for a cubic crystal

Abstract

We study wave interaction coefficients in elastic solids. They describe locally on a quadratically nonlinear level which waves interact and measure how strong the interactions are. We derive general formulas for these coefficients in an arbitrary anisotropic material expressing them in terms of the second and the third derivatives of the strain energy. To illustrate our results, we analyse the most symmetric class of cubic crystals calculating the coefficients at the zero constant states. We first investigate the geometrically nonlinear and materially linear solid and then we study the influence of material nonlinearities on the interaction coefficients. The obtained formulas are expressed in terms of elastic constants.