Interaction Of Elastic Inclusion And Crack In Half Space

The problems of SH-wave scattering, which are caused by elastic cylindrical inclusion and crack of arbitrary length and arbitrary position, are studied in this paper beyond the field of linearly elastic dynamic mechanics. The methods of Green's Function, complex variables and muti-polar coordinates are used here. Firstly we construct a suitable Green's function, which is an essential solution to the displacement field for the elastic half-space possessing elastic cylindrical inclusion while bearing out-of-plane harmonic line source load at arbitrary point. Then using the Green's function, the scattering problem of SH-wave is studied, which is caused by elastic cylindrical inclusion and crack of arbitrary length and arbitrary position. Then using the method of crack-division, the crack is established: reverse stresses are inflicted along the crack, that is, out-of-plane harmonic line source loads, which are equal in the quantity but opposite in the direction to the stresses produced for the reason of SH-wave scattering by crack and elastic cylindrical inclusion, are loaded at the region where crack will appear, thus the crack can be made out. Thus expressions of displacement and stress are established while crack and inclusion are both in existent. Finally, the dynamic stress concentration factor around the elastic cylindrical inclusion, the horizontal surface displacement and the variety of dynamic stress intensity factor at crack tip are discussed to the case of different parameters (the ratio of the wave number, the ratio of the shear modulus, the incident angle of SH-wave, the embedded depth of the elastic cylindrical inclusion and the position of crack).