Mechanics of indentation

An example of a nanoindentation in fused silica imaged using an atomic force microscope.

Although the indenter tip used in the experiment was nominally Hertzian (i.e. supposedly well approximated by a sphere or a paraboloid), the image clearly shows substantial deviation from this shape, which is more reminding of a blunted pyramid.

Yet the measured load-displacement response (when analysed properly) shows some excellent agreement with Hertz's solution! These results raise some very interesting questions about the influence of indenter geometry and the sensitivity of load-displacement traces to finite shape changes. Some of the answers can be found in anlytical form using the complex potential method by A.E.Green and W.Zerna (Theoretical Elsticity, sec.5.8, but also earlier by A.E.H.Love, W.D.Collins, etc.)