The basis of the quantitative conical/pyramidal (nano) indentation, without fittings, iterations, or simulations, is the physically founded FN=k h3/2 relation. The constant k (penetration resistance, mN/μm3/2) from linear plot with excellent regression discards initial surface effects, identifies important phase transformation onsets, conversion and activation energies, and reveals errors.
The failing Sneddon theory of ISO with unphysical exponent 2 on h lacks these possibilities, disregards shear-force work, and violates the first energy law since 50 years. The denied but strictly quantified loss of energy (20% for physical h3/2; 33.33% at believed h2) violates the first energy law and disregards the force remaining for penetration. Straightforward correction is performed for the dimensions, by replacing unphysical exponent 2.