Finite amplitude transverse waves in materials with memory

Abstract

We consider the propagation of finite amplitude plane transverse waves in a class of homogeneous isotropic incompressible viscoelastic solids with memory. 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 depends not only on current but also on previous deformations. The body is first subjected 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 finite amplitude circularly polarized waves 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.