Small Amplitude Plane Waves in Deformed Mooney—Rivlin Viscoelastic Solids

Abstract

A homogeneous isotropic incompressible viscoelastic material of differential type whose elastic part of the stress tensor is modelled through the use of the Mooney—Rivlin from of the stored energy function, and whose dissipative part is modelled as in a Newtonian fluid, is maintained in a state of finite static homogeneous biaxial deformation. The equations of superimposed infinitesimal motions on the finite deformation are derived. All propagating homogeneous and inhomogeneous solutions are given, as well as the conditions for linear, elliptical, or circular polarization.