Interactions of Plane Waves in Nonlinear Elasticity

We derive general formulas for the interaction coefficients of nonlinear plane waves propagating in any direction in an arbitrary hyperelastic medium. The formulas are expressed in terms of the derivatives of the strain energy and the eigensystem of the appropriate Hessian of the strain energy. Our methods clearly show the influence of geometrical and physical nonlinear-ities. We use our formulas to calculate the interaction coefficients for a general isotropic medium, both unstressed and prestressed. 1