Elastic wave propagation in simple-sheared hyperelastic materials with different constitutive models

TL;DR

This study explores elastic wave behavior in simple-sheared hyperelastic materials with different models, revealing how material properties and deformation influence wave modes and propagation, with implications for advanced metamaterials and wave control devices.

Contribution

It systematically analyzes wave modes in various hyperelastic models under shear, highlighting conditions for pure and quasi modes and their dependence on material parameters.

Findings

Pure elastic wave modes in compressible neo-Hookean materials.

Quasi modes with abnormal ray directions in reformulated models.

Material constants and deformations significantly affect wave propagation.

Abstract

We investigate the elastic wave propagation in various hyperelastic materials which subjected to simple-shear deformation. Two compressible types of three conventional hyperelastic models are considered. We found pure elastic wave modes can be obtained in compressible neo-Hookean materials constructed by adding a bulk strain energy term to the incompressible strain energy function. Whereas for the compressible hyperelastic models which are reformulate into deviatoric and hydrostatic parts, only quasi modes can propagate, with abnormal ray directions can be observed for longitudinal waves. Moreover, the influences of material constants, material compressibility and external deformations on the propagation and refraction for elastic waves in these hyperelastic models are systematically studied. Numerical simulations are carried out to validate the theoretical results. This investigation may open a promising route for the realization of next generation metamaterials and novel wave manipulation devices.