Scattering of SH wave by an elliptic hole: surface effect and dynamic stress concentration

This paper studies the stress concentration around an elliptical hole embedded in an elastic medium under a far-field incident harmonic SH wave. Compared with related existing studies in the literature, the current study particularly incorporates surface elasticity effects in case the size of the hole falls within the micro- or lower-scale. The elliptic coordinate system and the Mathieu functions are introduced to solve the corresponding boundary value problem, and a series-form solution is obtained for the full-field scattering wave function. The dynamic stress concentration around the hole induced by the far-field incident wave is illustrated via a group of numerical examples. It is shown that the surface effect suppresses the fluctuation of the dynamic stress distribution around the hole and reduces significantly the dynamic stress concentration around the hole at the micro- or lower-scale.

Automated summary

This paper investigates the stress concentration around an elliptical hole in an elastic medium, taking into account the surface elasticity effects. The problem is solved using the elliptic coordinate system and Mathieu functions, and a series-form solution is obtained. Numerical examples are presented to illustrate the dynamic stress concentration induced by the far-field incident wave. The results show that the surface effect suppresses stress fluctuations and significantly reduces the dynamic stress concentration at the micro- or lower-scale.