Finite-amplitude inhomogeneous plane waves of exponential type in incompressible elastic materials

TL;DR

This paper proves that elliptically-polarized finite-amplitude inhomogeneous plane waves cannot propagate in incompressible isotropic elastic materials, regardless of initial stress or deformation, due to the incompressibility constraint.

Contribution

It establishes a fundamental limitation on wave propagation in incompressible elastic materials, extending understanding of wave behavior under finite amplitudes.

Findings

Elliptically-polarized inhomogeneous waves cannot propagate in incompressible materials.

The result is valid for both stress-free and deformed states.

Wave attenuation occurs in a direction different from propagation.

Abstract

It is proved that elliptically-polarized finite-amplitude inhomogeneous plane waves may not propagate in an isotropic elastic material subject to the constraint of incompressibility. The waves considered are harmonic in time and exponentially attenuated in a direction distinct from the direction of propagation. The result holds whether the material is stress-free or homogeneously deformed.