Large acoustoelastic effect

TL;DR

This paper extends classical acoustoelasticity to include fourth-order elasticity constants by coupling small-amplitude waves with finite pre-deformations, enabling non-destructive evaluation of higher-order elastic properties.

Contribution

It introduces a method to determine fourth-order elasticity constants using small waves and finite pre-deformations, linking nonlinear elasticity with high-pressure physics.

Findings

Demonstrates coupling of small waves with finite pre-deformation to measure fourth-order constants

Provides a theoretical framework for weakly nonlinear elasticity in compressible materials

Connects acoustoelasticity with high-pressure physics through Bridgman's results

Abstract

Classical acoustoelasticity couples small-amplitude elastic wave propagation to an infinitesimal pre-deformation, in order to reveal and evaluate non-destructively third-order elasticity constants. Here, we see that acoustoelasticity can be also be used to determine fourth-order constants, simply by coupling a small-amplitude wave with a small-but-finite pre-deformation. We present results for compressible weakly nonlinear elasticity, we make a link with the historical results of Bridgman on the physics of high pressures, and we show how to determine "D", the so-called fourth-order elasticity constant of soft (incompressible, isotropic) solids by using infinitesimal waves.