I think you are talking about a beam made of a bi-modulus material as you mention 'neutral exis'. For a beam, the location of the neutral axis depends on the ratio of this 2 moduli and is independent of the load applied.
The normal stress is equal at zero in the neutral axis. So the position of this axe depend of the loading (normal loading). The mean axis doesn't depend of the loading and pass by the gravity center of the beam (this axis depends of young modulus for a bimodulus material).
In the case of a rectangular bar bent by terminal transverse load, the neutral axis shift consists of two terms: a constant term (depending on the Young's modules) minus a term proportional to the applied load.