Effect of interfacial stress on the reflection and transmission of in-plane waves

The mechanical properties of the interfacial region are quite different from those of the adjacent bulk materials. By employing the Gurtin–Murdoch surface elasticity model, we investigated the reflection and transmission of in-plane waves (P- and SV-waves) at an interface separating two elastic half-spaces. We derived a system of eight equations for the amplitudes and phase shifts of the reflected and transmitted waves. Furthermore, interfacial regions may contain various types of microstructures. By modeling the interface between two materials as a microstructured Kirchhoff thin plate and adopting the Aifantis strain-gradient model to characterize its mechanical behavior, we developed a strain-gradient thin plate model. This model extends the Gurtin–Murdoch surface elasticity framework due to the incorporation of strain-gradient effect. By using the newly established strain-gradient thin plate model, we revisited the in-plane wave reflection/transmission problem. Additionally, we conducted parametric studies to show how interfacial parameters and strain-gradient constant affect the reflection and transmission coefficients for in-plane wave incidence. This study can provide insights for the design of ultrasonic signal processing devices that utilize thin films as surface/interface waveguides.