With increasing force P, not only the characteristic size of the locally deformed region changes, but also the ratio between elastic and plastic deformation, as well as the atomic mechanisms of plastic deformation. Therefore, theory and model concepts must be consistent with these changes. At the initial stages of the immersion of the indenter, the entire deformation is purely elastic and can be calculated using the theories of contact elasticity (for example, according to G. Hertz).
Exceeding the triggering voltage of defect sources causes the nucleation of interstitial atoms and their low-atomic clusters such as crowdions, dislocation loops, nanotwins, and other nanoscale objects. At this stage, the theory of nucleation and mobility of isolated structural defects in a field of specified elastic stresses is applicable (for example, the theory of dislocations). A further increase in P causes significant plastic deformation, which significantly distorts the elastic stress field under the indenter. In this case, it is necessary to simultaneously take into account both elastic and plastic deformation under the contact area (for example, by the finite element method), since their contribution to the total deformation becomes comparable. Finally, an even greater increase in P leads to the formation of an imprint, in which elastic deformation in the first approximation can be neglected due to its small fraction.