[00861] Using elastic waves to measure mechanical stress
Session Time & Room : 5D (Aug.25, 15:30-17:10) @E812
Type : Contributed Talk
Abstract : In principle, elastic waves could be used to assess the stress in a material, as the higher the stress, the faster the wave will propagate. However, the speed also depends on material parameters, which is why there are no robust (non-invasive) measurement techniques. In this talk we show how to overcome these challenges by using universal relationships between stress and wave speeds. This has led to robust measurements with either bulk waves [2] or surface waves [3].
Universal relationships in continuum mechanics are those that hold for any type of material, or constitutive choice [1]. To measure stress, it would be ideal to have a relationship between the wave speed and the stress that holds for any elastic material. However, there is only one such universal relationship: $\rho v_{12}^2 - \rho v_{21}^2 = \sigma_{11} - \sigma_{22}$, where $\sigma_{ij}$ are the components of the Cauchy stress tensor, and $v_{12} (v_{21})$ is the speed of a shear wave propagating in the $x_1 (x_2)$ direction that is polarised in the $x_2 (x_1)$ direction. Inspired by this identity we propose, and experimentally validate, several new ultrasonic methods.
[1] Truesdell, Clifford, and Walter Noll. "The non-linear field theories of mechanics." The non-linear field theories of mechanics. Springer, Berlin, Heidelberg, 1992. 1-579.
[2] Li, Guo-Yang, Artur L. Gower, and Michel Destrade. "An ultrasonic method to measure stress without calibration: The angled shear wave method." The Journal of the Acoustical Society of America 148.6 (2020): 3963-3970.
[3] Li, Guo-Yang, et al. "Non-destructive mapping of stress and strain in soft thin films through sound waves." Communications Physics 5.1 (2022): 1-7.
