The P-h2 relationship in indentation

In this paper we derive an analytical expression for the indentation load-depth relation during loading in an indentation experiment, namely P = E-r(1/root C root E-r/H + epsilon root pi/4 root H/E-r)(-2) (h + xi)(2). The advantage over previously used expressions is that no additional empirical constants are necessary. A comparison between the new expression and results from finite element calculations shows excellent agreement.