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

TL;DR

This paper investigates finite-amplitude inhomogeneous plane waves in a deformed Mooney-Rivlin material, revealing conditions for wave propagation and deriving new static solutions, with energy flux results matching classical linear elasticity.

Contribution

It provides the first analysis of finite-amplitude inhomogeneous waves in a Mooney-Rivlin material and introduces new exact static solutions.

Findings

Waves occur when normals to phase and amplitude planes are orthogonal and conjugate with respect to the B-ellipsoid.

Energy flux results match those of classical linearized elasticity despite non-linearity.

New exact static solutions for the Mooney-Rivlin material are derived.

Abstract

The propagation of finite-amplitude linearly-polarized inhomogeneous transverse plane waves is considered for a Mooney-Rivlin material maintained in a state of finite static homogeneous deformation. It is shown that such waves are possible provided that the directions of the normal to the planes of constant phase and of the normal to the planes of constant amplitude are orthogonal and conjugate with respect to the B-ellipsoid, where B is the left Cauchy-Green strain tensor corresponding to the initial deformation. For these waves, it is found that even though the system is non-linear, results on energy flux are nevertheless identical with corresponding results in the classical linearized elasticity theory. Byproducts of the results are new exact static solutions for the Mooney-Rivlin material.