  This paper presents a generalization of Murnaghan elastic material to
viscoelastic behavior using the Green-Rivlin multiple-integral approach. In the
linear limit, the model coincides with the generalized Maxwell model. To create
a nonlinear generalization, all possible second-order corrections were included
in the constitutive equations written in the internal strains representation.
Using this approach, we obtained expressions for the time- and
frequency-dependent nonlinear dynamic moduli. We applied the developed
nonlinear viscoelastic model to the description of infinitesimal strain waves
superposed on finite prestrain. Furthermore, we considered the generation of
higher harmonic by the nonlinear interaction of two strain waves, which we
showed can provide a method to measure all viscoelastic constants of the
developed model.
