Generalization of nonlinear Murnaghan elastic model for viscoelastic materials

Abstract

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 a finite prestrain. Furthermore, we considered the generation of higher harmonics by the nonlinear interaction of two strain waves, which we showed can provide a method for measuring all viscoelastic constants of the developed model.