  For cylindrical indentation of elastic half-space the relationship between
the depth of indentation delta and the applied force F is nonlinear, in
contrast to the linear relationship between the height of the contact zone
delta_0 and the force F. While the latter is independent of the boundary
conditions used to specify the rigid-body translation, the former depends on a
selected datum for vertical displacement. The depth of the indentation is
determined for any permissible value of the length b, which specifies the
points of the free surface where the vertical displacement is required to be
zero, w(b)=0. From the condition that the work of the indentation force is
equal to the work of the contact pressure, it follows that the indentation is
geometrically and physically possible under imposed boundary conditions w(b)=0
provided that b>=b_min. The numerical value of b_min is found to be about 10
times greater than the semi-width of the contact zone a, based on the numerical
precision in fulfilling the work condition W_F=W_p. If a datum is taken to be
at a point at some distance h below the load, there is an alternative
closed-form expression for delta in terms of F, which involves the Poisson
ratio nu. For nu=1/3, it is found that h_min is about 21a. A simple expression
relating the permissible values of h and b is derived, which is linear for
large values of h and b.
