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 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.

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• Medium Amplitude Parallel Superposition (MAPS) Rheology, Part 1: Mathematical Framework and Theoretical Examples
• Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals
• Proper formulation of viscous dissipation for nonlinear waves in solids
• Nonlinear elastic moduli of composite materials with nonlinear spherical inclusions dispersed in a nonlinear matrix