Circularly polarized wave propagation in a class of bodies defined by a new class of implicit constitutive relations

Abstract

In this paper, we show that circularly polarized transverse stress waves, standing shear stress waves, and oscillatory shear stress waves can propagate in a new class of viscoelastic solid bodies which are a subclass of bodies described by implicit constitutive theories. The class of models that is being considered includes as sub-classes, the classical Kelvin–Voigt model, the new models introduced by Rajagopal wherein the Cauchy–Green tensor is a non-linear function of the stress, and the Navier–Stokes fluid model. The solutions established in this paper are generalizations of solutions that have been established within the context of nonlinear elasticity by Carroll, and Destrade and Saccomandi, to the new class of elastic and viscoelastic bodies that are being considered.