Small amplitude waves and stability for a pre-stressed viscoelastic solid

TL;DR

This paper analyzes how small amplitude waves propagate and affect stability in pre-stressed viscoelastic solids, with implications for medical imaging techniques that utilize tissue deformation.

Contribution

It provides bounds on parameters and pre-deformation levels that guarantee linearized stability in nonlinear viscoelastic materials.

Findings

Bounds on constitutive parameters ensuring stability

Pre-deformation enhances contrast in tissue imaging

Analysis of bulk and surface wave dissipation

Abstract

We study the propagation of small amplitude waves superimposed on a large static deformation in a nonlinear viscoelastic material of differential type. We use bulk waves and surface waves to address the questions of dissipation and of material and geometric stability. In particular, the analysis provides bounds on the constitutive parameters and on the pre-deformation that ensure linearized stability in the neighbourhood of a large pre-stretch. This type of result is relevant to the imaging of biological soft tissues using acoustical techniques, where pre-deformation is known to increase contrast and reduce de-correlation noise.