492 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1952 



6.0 

 5.5 

 5.0 

 4.5 

 4.0 

 3.5 

 3.0 

 2.5 

 2.0 

 1.5 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 

 RATIO OF p/a 



Fig. 16 — Traction plotted against radius for elastic displacement and modifi- 

 cation introduced by the effect of slip. 



contact theory is 



V = 



2ira- 



1 - 



r- 



(15) 



Mindlin assumes that sKp takes place bet^veen the two surfaces until 

 the tangential traction is equal to 



-^ - Hi/' 



for a' < p < a 



(16) 



and less than this for all interior points, \vhere in this equation p is the 

 radius vector and a' the inner radius for which slip stops. This corre- 

 sponds to the introduction of a new system of forces and Mindlin has 

 shown that equilibrium is reestablished when the surface tractions are 

 given by Equation (16) when a' < p ^ a and by 



X, = 



27ra2 



W' 



when p < a' (17) 



Fig. 16 shows this distribution for the case T/fN = 0.3. The inner radius 

 a' is given such a value that the integrated traction over the surface 



