Elastic Field of a Hemispherical Inhomogeneity at the Free Surface of an Elastic Half Space

摘要

This paper analyses the elastic fields around a hemispherical inhomogeneity at the free surface of a semi-infinite elastic body. The loading is either all-around tension at infinity, perpendicular to the axis of symmetry of the inhomogeneity or uniform eigenstrains introduced in the inhomogeneity. The interface between the inclusion and the matrix assumes perfect bonding, shear-traction-free sliding or intermediate between them. A spring-type resistance model is used to investigate this intermediate stage. The method of Boussinesq's displacement potentials is used in the analysis and the solution is expressed in terms of five sets of spherical harmonics. Numerical calculations are performed to illustrate the results. It was found that the non-vanishing stress components at the free surface of the inclusion are constant for equal Poisson's ratios. Reprints. (JHD)