Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion

Abstract

This paper focuses on analyzing SH-wave scattering around a circular nanoinclusion using the complex variable function method. The surface elasticity theory is employed in the analysis to account for the interface effect at the nanoscale. Considering the interface effect, the boundary condition is given, and the infinite algebraic equations are established to solve the unknown coefficients of the scattered and refracted wave solutions. The analytic solutions of the stress field are obtained by using the orthogonality of trigonometric function. Finally, the dynamic stress concentration factor and the radial stress of a circular nanoinclusion are analyzed with some numerical results. The numerical results show that the interface effect weakens the dynamic stress concentration but enhances the radial stress around the nanoinclusion; further, we prove that the analytic solutions are correct.

Dynamic Stress around a Cylindrical Nano-Inclusion with an Interface in a Right-Angle Plane under SH-Wave

“…As s increases, the DSCF decreases. e maximum stress concentration occurred at θ � π/2 and θ � 3π/2, and the minimum stress concentration occurred at θ � 0, θ � π, and θ � 2π, which are quite similar to the results of previous research [15][16][17][18][19][20][21][22][23][24].…”

“…For a macroscopic inclusion, the value of R is big enough (s ≪ 1), and thus, the surface effect s can be ignored. However, when the radius R of the inclusion shrinks to the nanoscale, s becomes noticeable and the surface effect should be considered [15][16][17][18][19][20][21][22][23][24].…”

“…Substituting equations (18), (22), and (23) into equations (30) and 35, then multiply e − imθ on both sides of the equations, and then apply integral from 0 to 2π, we have a m H (1)…”

“…Furthermore, Ru et al [19][20][21] studied elastic wave's diffraction by a cluster of nanosized cylindrical holes. Using the complex variable function theory, Wu [22] discussed the interface effects of SH-waves' scattering around a cylindrical nano-inclusion.…”

Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity

“…Ru et al [21][22][23] studied the di raction of the elastic waves around a cylindrical nano-inclusion and then studied the surface e ects of the scatterings of the vertical shear wave by a cluster of nanosized cylindrical holes. Wu and Ou [24,25] studied the interface e ects of SH-waves' scattering around a cylindrical nano-inclusion by wave functions expansion method and complex variable function theory respectively. However, thanks to the complex boundary conditions of the arbitrary shaped cavity, most of those studies are con ned to the circular hole or the spherical cavity/inclusion at the nano-size.…”