Indentation of soft material containing filler particles

Abstract

The work is devoted to the study of the features of the interaction of the atomic force microscope probe with a soft elastomeric material containing hard particles of nanofiller. In experimental studies of materials using the nanoindentation mode of AFM, the main result is the curves describing the dependence of the cantilever bend on the probe penetration depth. The indentation can be carried out on a set of points on the material surface and a map of the stiffness distribution can be obtained. The semi-contact mode is most often used in practice to study the relief of an elastomeric nanocomposite. To obtain a correct interpretation of the data, the use of mathematical models is required. An important element of these models is the dependence of the elastic resistance force on the depth of the probe penetration into the material.The paper presents solutions to the problems of indentation of Neo-Hookean material in the formulation of plane deformations. The inclusions were presented as round particles. Solutions are obtained for the cases of indentation near filler particles of different sizes and with different depths of their location under the surface. Computational experiments have shown that by the response to the probe indentation into the material, we can obtain additional information (about the shape and depth of the inclusions), which can be used in the analysis of the material structure data maps.