Sh-wave Scattering By Elliptical Inclusion And Crack In Half-space

The methods of Green’s function, complex variable function and multi-polar coordinatesare applied in this paper to report interaction of elliptical elastic inclusion and an arbitrarylength of crack at any position under incident SH-waves. Furthermore, two circumstances arerespectively investigated: SH-waves are incident vertically from upside and with any anglefrom downside in infinite half-space.Firstly, combined with the symmetry of SH-waves scattering, the "conformal mapping"technology of complex variable functions and the method of multi-polar coordinate aredeveloped to construct a Green’s function, the fundamental solution to the displacement fieldfor elastic half space containing elliptical inclusion while bearing out-plane line source load atarbitrary point, which will be utilized to create a beeline crack with arbitrary length at anyposition based on “crack-division” technology: at the region where the crack appears, theloads the same in magnitude but opposite in sign to the stresses produced by SH-wavesscattering are inflicted, then the total stresses will be zero, namely, a crack is created. Thenthe displacement field and stress field of elastic half-space possessing elliptical elasticinclusion and a crack can be deduced and thus the analytical expressions of dynamic stressconcentration factor (DSCF) around the elastic inclusion and dynamic stress intensity factor(DSIF) at crack tip can be also derived. Lastly, numerical examples are presented to analyzeand discuss the dependence of dynamic stress concentration factor (DSCF) around theelliptical inclusion, the horizontal surface displacement and dynamic stress intensity factor(DSIF) at crack tip on different parameters, including the incident wave number, the incidentangle, the embedded depth of elastic inclusion, the ratio of wave number, the ratio of shearmodulus, the position of crack and the shape of inclusion.