Mechanics of deformable solids Definition

Acoustoelastic effect

Builds on Elastodynamics Hyperelastic material Linear elasticity

Definition

Let a hyperelastic solid be held in a static, possibly finite, deformation, called the initial or pre-stressed state, with initial stress $\sigma^0$ . Superpose on it a small time-dependent displacement and linearize the equations of motion about the initial state. The result is a linear elastodynamic system whose effective coefficients depend on $\sigma^0$ . The acoustoelastic effect is the dependence of the speeds of plane waves of this incremental system on the initial stress $\sigma^0$ .

Remarks

For small initial strain the change of each wave speed is, to first order, a linear function of the initial stress. Its coefficients involve the second-order (Lamé) constants and the third-order elastic constants of the material, for example the Murnaghan constants $l, m, n$ of an isotropic solid.

Example: a steel bar under uniaxial tension carries longitudinal ultrasonic waves along its axis at a speed slightly different from the unstressed value. For small stress the relative change grows linearly with the stress.

Non-example: in a material described by linear elasticity the wave speeds are fixed by $\lambda$ , $\mu$ and $\rho$ alone. Within that linear model a static load does not change them.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Tag	`TNDKHZBVXV`
URI	`m2://TNDKHZBVXV`
Kind	definition
Writing	W0 stub
MSC	74J05, 74B10, 74B15
Defines	Acoustoelastic effect
Uses	Elastodynamics, Hyperelastic material, Linear elasticity
Changed	3 November 2026

Acoustoelastic effect

Definition

Remarks

Reading path

Further reading

What this page needs for W1

What links here