Abstract
This paper presents an analytical solution for an infinite body having a spherical inclusion when the body is subjected to bending at infinity. In this analysis, two types of inclusions, i.e., a perfectly bonded inclusion (displacements and tractions are continuous) and a slipping inclusion (tractions and normal displacements are continuous and shear traction vanishes) are discussed. The solution is based on the Dougall' s displacement potentials approach and the associated Legendre harmonic functions of first kind are employed by considering the regularity of the space. The solutions for the matrix and the inclusion, consist of linear combination of the associated Legendre functions, are determined by the boundary conditions on the interface. The numerical solutions are represented in the form of graphs and the effects of the inclusions on the stress distribution are clarified. From the analyzed results, it is found that the stresses around the inclusion are considerably affected by the interface conditions.
