Experimental and numerical investigations on the acoustoelastic effect in hyperelastic waveguides

Guided ultrasonic wave based structural health monitoring has been of interest over decades. However, the influence of pre-stress states on the propagation of Lamb waves in thin-walled structures is not fully covered, yet. So far experimental work presented in the literature only focuses on a few individual frequencies, which does not allow a comprehensive verification of the numerous numerical investigations. Furthermore, most work is based on the strain-energy density function by Murnaghan. To validate the common modeling approach and to investigate the suitability of other non-linear strain-energy density functions an extensive experimental and numerical investigation covering a large frequency range is presented here. The numerical simulation comprises the use of the Neo-Hooke as well as the Murnaghan material model. It is found that these two material models show qualitatively similar results. Furthermore, the comparison with the experimental results reveals, that the Neo-Hooke material model reproduces the effect of pre-stress on the difference in the Lamb wave phase velocity very well in most cases. For the $A_0$ wave mode at higher frequencies, however, the sign of this difference is only correctly predicted by the Murnaghan model. In contrast to this the Murnaghan material model fails to predict the sign change for the $S_0$ wave mode.