Abstract
A new model of the interaction of AFM sharp probe with a soft incompressible elastic material is proposed. The model takes into account the finite deformations of the material. The novelty is the consideration of bending and increasing of the material-air interface during the process of indentation. The work performed by the probe is spent both on the elastic deformation of the sample and on changing the geometry of the material-air interface. The paper proposes an explanation of possibility to simulate the phase boundary by a thin elastic layer under the condition of its large shrinkage. The obtained approximation dependences allow quick computer calculations. The presented arguments justify the possibility of neglecting the probe jump to the sample surface. It is established that the Deryagin-Muller-Toporov model is a special case of the proposed model.
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