  Nanoindentation is a widely used method for sensitive exploration of the
mechanical properties of micromechanical systems. We derived an empirical
analysis technique to extract stress-strain field gradient and divergence
representations from nanoindentation measurements. With this approach local
gradients and heterogeneities can be discovered to obtain more detail about the
sample's microstructure, thus enhancing the analytic capacity of the
nanoindentation technique. We analysed nanoindentation tests of bulk solid
substrates, namely bearing and tooling steel, and fused silica. Oscillations of
the stress-strain field gradient and divergence induced in the subsurface layer
by the nanoindentation experiment were revealed. The oscillations were
especially prominent in single measurements at low indentation depths (< 100
nm), whereas they were concealed in the averaged datasets. The amplitude of
stress-strain field divergence oscillations decayed as a sublinear power-law
when the indenter approached deeper atomic layers, with an exponent -0.9 for
the steel and -0.8 for the fused silica. The oscillations were interpreted as
alternating strain hardening-softening cycles induced in the subsurface layers
under the indenter load. A selective assessment of elastic and plastic
stress-strain field components indicated an elastic-plastic deformation process
where the normal strain is transformed into the shear strain leading to a
plastic deformation.
