Looking through books and papers I see an often quoted equation to show that the contact radius (a) of spherical indenter of radius (R) is related to the indentation depth (h):

a= √(R.h)

However, using simple trigonometry of a spherical cap it can be shown that:

a=√(2Rh-h2)

Contact area is very important for use in nanoindentation - however, if it is based on the wrong contact area calculation, then more errors become apparent.

On that note - I also want to ask if a rigid flat indenter press on a thin shell sphere, is the contact radius the same as a rigid spherical indenter pressing on a flat surface ?

Colin