Using the general solution forms of Exercise 13.22, solve the problem of a rigid spherical inclusion of radius a perfectly bonded to the interior of an infinite body subjected to uniform stress at infinity of σ^∞_R = S. Explicitly show that the stress field is given by:

Determine the nature of the stress field for the incompressible case with v = 1/2. Finally, explore the stresses on the boundary of the inclusion (R = a), and plot them as a function of Poisson’s ratio.

Data from exercise 13.22

Using the basic field equations for spherical coordinates given in Appendix A, formulate the elasticity problem for the spherically symmetric case, where u_R = u(R), u_∅ = u_θ = 0. In particular, show that the governing equilibrium equation with zero body forces becomes:

1 - 2v 1-2v OR=S[1 +2= # (2)]. * - 0$ - $[1-1- = 1+v 1+v = (2)