Finite amplitude inhomogeneous waves in Mooney-Rivlin viscoelastic solids

TL;DR

This paper presents exact solutions for finite-amplitude inhomogeneous waves in Mooney-Rivlin viscoelastic solids, revealing new wave behaviors including damped traveling and standing waves due to viscous effects.

Contribution

It introduces novel exact solutions for inhomogeneous waves in Mooney-Rivlin viscoelastic materials, extending elastic wave theory to viscoelastic contexts with new wave phenomena.

Findings

Similar geometric conditions as elastic case for wave planes

New solutions for neo-Hookean and Newtonian fluids include damped waves

Viscous effects enable standing and traveling damped wave solutions

Abstract

New exact solutions are exhibited within the framework of finite viscoelasticity. More precisely, the solutions correspond to finite-amplitude, transverse, linearly-polarized, inhomogeneous motions superposed upon a finite homogeneous static deformation. The viscoelastic body is composed of a Mooney-Rivlin viscoelastic solid, whose constitutive equation consists in the sum of an elastic part (Mooney-Rivlin hyperelastic model) and a viscous part (Newtonian viscous fluid model). The analysis shows that the results are similar to those obtained for the purely elastic case; inter alia, the normals to the planes of constant phase and to the planes of constant amplitude must be orthogonal and conjugate with respect to the B-ellipsoid, where B is the left Cauchy-Green strain tensor associated with the initial large static deformation. However, when the constitutive equation is specialized either to the case of a neo-Hookean viscoelastic solid or to the case of a Newtonian viscous fluid, a greater variety of solutions arises, with no counterpart in the purely elastic case. These solutions include travelling inhomogeneous finite-amplitude damped waves and standing damped waves.