Finite Amplitude Transverse Waves in Special Incompressible Viscoelastic Solids

We consider the propagation of finite amplitude plane transverse waves in a class of homogeneous isotropic incompressible viscoelastic solids. It is assumed that the Cauchy stress may be written as the sum of an elastic part and a dissipative viscoelastic part. The elastic part is of the form of the stress corresponding to a Mooney–Rivlin material, whereas the dissipative part is a linear combination of A ₁, A ₁ ² and A ₂, where A ₁, A ₂ are the first and second Rivlin–Ericksen tensors. The body is first subject to a homogeneous static deformation. It is seen that two finite amplitude transverse plane waves may propagate in every direction in the deformed body. It is also seen that a finite amplitude circularly polarized wave may propagate along either n ⁺ or n ^?, where n ⁺, n ^? are the normals to the planes of the central circular section of the ellipsoid x?B ^?1 x=1. Here B is the left Cauchy–Green strain tensor corresponding to the finite static homogeneous deformation.