On the accuracy of one-way approximate models for nonlinear waves in soft solids

TL;DR

This paper introduces and analyzes one-way approximate models for nonlinear shear waves in soft solids, highlighting their accuracy and limitations in capturing wave behavior, especially at larger amplitudes.

Contribution

It derives exact nonlinear viscous wave equations and one-way Burgers-type equations, providing insights into their accuracy and applicability in modeling nonlinear wave propagation in soft solids.

Findings

Distinct solutions from different PDE models

Deviations increase with wave amplitude

Elastic limit links to shock wave theory

Abstract

Simple strain-rate viscoelasticity models of isotropic soft solid are introduced. The constitutive equations account for finite strain, incompressibility, material frame-indifference, nonlinear elasticity, and viscous dissipation. A nonlinear viscous wave equation for the shear strain is obtained exactly, and corresponding one-way Burgers-type equations are derived by making standard approximations. Analysis of the travelling wave solutions shows that these partial differential equations produce distinct solutions, and that deviations are exacerbated when wave amplitudes are not arbitrarily small. In the elastic limit, the one-way approximate wave equation can be linked to simple wave theory and shock wave theory, thus allowing direct error measurements.