Small-amplitude inhomogeneous plane waves in a deformed Mooney-Rivlin material

TL;DR

This paper analyzes the propagation of small-amplitude inhomogeneous plane waves in a deformed Mooney-Rivlin material, revealing a variety of solutions including novel circular and linear polarization cases with complex propagation characteristics.

Contribution

It provides a comprehensive set of solutions for inhomogeneous wave propagation in deformed Mooney-Rivlin materials, including new types of polarized waves and their conditions.

Findings

Existence of circularly-polarized plane waves with arbitrary complex slowness

Linearly-polarized waves with non-orthogonal propagation and attenuation directions

A variety of solutions with geometrical interpretations and explicit examples

Abstract

The propagation of small-amplitude inhomogeneous plane waves in an isotropic homogeneous incompressible Mooney--Rivlin material is considered when the material is maintained in a state of finite static homogeneous deformation. Disturbances of complex exponential type are sought and all propagating inhomogeneous solutions to the equations of motion are given, as well as the conditions for linear, elliptical, or circular polarization. % It is seen that a great variety of solutions arises. These include some original solutions, such as circularly-polarized plane waves which propagate with an arbitrary complex scalar slowness, or linearly-polarized waves for which the direction of propagation is not necessarily orthogonal to the direction of attenuation. % Throughout the paper, geometrical interpretations and explicit examples are presented.