Dynamic stress from a subsurface cylindrical inclusion in a functionally graded material layer under anti-plane shear waves

The multiple scattering of shear waves and dynamic stress resulting from a subsurface cylindrical inclusion in a functionally graded material (FGM) layer bonded to homogeneous materials are investigated, and the analytical solution of this problem is derived. Image method is used to satisfy the traction free boundary condition of the FGM layer. The analytical solutions of wave fields around the actual and image inclusions are expressed by employing wave functions expansion method, and the expanded mode coefficients are determined by satisfying the continuous boundary conditions around the inclusions. Through the numerical solutions of dynamic stress concentration factors (DSCFs) around the inclusion, the effects of the position of the inclusion in the material layer, the properties of the inclusion, and the properties of the two phases of composites on the DSCFs are analyzed. Analyses show that when the cylindrical inclusion is stiffer than the two phases of FGMs, the dynamic stress around the inclusion increases greatly. When the distance between the surface of the structure and the inclusion is smaller, the effect of the properties of the inclusion becomes greater. When the cylindrical inclusion is softer than the two phases of FGMs, the maximum dynamic stress shows little difference; however, the variation of the distribution of the dynamic stress around the inclusion is greater.