Ball and socket contact stresses

[cabellos6]

I am familiar with Hertzian contact mechanics for spheres in contact with a falt surface or a sphere in contact with another sphere. However, I am unsure on how to model a ball and socket contact? Could anyone help me with this idea please?

Thanks

 

[FredGarvin]

Sorry it took so long on this. I apparently forgot how to read.

According to the bible, Roark's, for a ball and socket:

The max compressive stress is:

\sigma_c = .918\left[ \sqrt[3]{\frac{P}{K_D^2 C_E^2}}\right]

Where:
P=the compressive load applied
K_D= Load condition factor = \frac{D_1D_2}{D_1-D_2}
D_1= Diameter of the socket
D_2= Diameter of the ball
C_E= \left[\frac{1-\nu_1^2}{E_1}\right]+\left[\frac{1-\nu_2^2}{E_2}\right]
E, \nu = Modulus of elasticity and Poisson's Ratio

Also, don't forget that the maximums for Hertzian stresses do not occur at the surface of the bodies.