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 a ssumed 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) ar e the first and second Rivlin-Ericksen tensors. The body is first subject t o a homogeneous static deformation. It is seen that two finite amplitude tr ansverse plane waves may propagate in every direction in the deformed body. It is also seen that a finite amplitude circularly polarized wave may prop agate along either n(+) or n(-), where n(+), n(-) are the normals to the pl anes 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 hom ogeneous deformation.