Reflection and transmission of elastic waves at the interface between two gradient-elastic solids with surface energy

• The dipolar elastic solids with surface energy are considered.
• The surface effects on reflection and transmission waves are considered.
• Both normal and oblique incident waves are considered.
• Both P and SV incident waves are considered.
• Non-traditional interface conditions with dipolar tractions are considered.

The reflection and transmission of an incident plane wave at an interface between two gradient elastic solids with surface energy are studied. First, some functions of strain energy density with the surface effects taken into consideration are postulated and the surface effects of gradient elastic solid are incorporated into the constitutive relations. Then, the nontraditional interface conditions by requiring the auxiliary monopolar tractions and the auxiliary dipolar tractions continuous across the interface are used to determine the reflection and transmission coefficients. Some numerical results of the reflection and transmission coefficient in terms of energy flux ratio are given for different microstructure parameters and surface parameters. The microstructure effects and the surface energy effects on the reflection and transmission waves are discussed based on the numerical results. It is found that the microstructure effects result in the appearance of two surface waves and the surface energy effects have apparent different influence on the body waves in gradient elastic solids and the surface waves at the interface. However, this phenomenon becomes pronounced only when the incident wavelength is close to the characteristic length of microstructure.