Constant Amplitude Acceleration Waves in a Prestrained Incompressible Isotropic Elastic Solid

It is known that all transverse plane acceleration waves that propagate through a homogeneously deformed Mooney Rivlin material do so without a change in amplitude. Here it is shown that the MooneyRivlin material is the only incompressible isotropic hyperelastic material that permits transverse plane acceleration waves to propagate in any direction without a change in amplitude, regardless of the homogeneous prestrain.