Finite-amplitude inhomogeneous plane waves in a deformed Mooney-Rivlin material

The propagation of finite-amplitude linearly-polarized inhomogeneous transverse plane waves is considered for a Mooney-Rivlin material maintained in a state of finite static homogeneous deformation. It is shown that such waves are possible provided that the directions of the normal to the planes of constant phase and of the normal to the planes of constant amplitude are orthogonal and conjugate with respect to the B-ellipsoid, where B is the left Cauchy-Green strain tensor corresponding to the initial deformation. For these waves, it is found that even though the system is non-linear, results on energy flux are nevertheless identical with corresponding results in the classical linearized elasticity theory. Byproducts of the results are new exact static solutions for the Mooney-Rivlin material.