A universal formulation for indentation whatever the indenter geometry

• A geometrical equivalence between conical and parabolic indentation is proposed.
• A new geometrical parameter for parabolic, spherical and conical indenter is proposed.
• A new pile-up function is also proposed for these three indenters geometries.
• Using these new functions allows a superposition of indentation results.

We propose in this paper a geometrical equivalence between a shape described by a power law and a conical geometry. A theoretical and numerical study has allowed us to generalize an equivalence between the conical geometrical parameter tanβ and the spherical or power law shape geometrical parameter ac/R. Moreover, in order to superpose indentation data whatever the geometry, a new pile-up parameter Δ has been introduced. For one set of mechanical properties of the tested sample, this new formulation leads to a perfect superposition between conical, power law shape and spherical indentation data. At the end of this paper, we propose a comparison between the results proposed in literature and the present formulation.