Generalization of nonlinear Murnaghan elastic model for viscoelastic materials

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...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Garbuzov, F E, Beltukov, Y M
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.05.2023
Subjects
Constitutive equations
Constitutive relationships
Nonlinear dynamics
Viscoelastic materials
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422