PSI - Issue 32

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Procedia Structural Integrity 32 (2021) 87–92

XXIIth Winter School on Continuous Media Mechanics Indentation of soft material containing filler particles Izyumov R.I. a *, Sokolov A.K. a , Svistkov A.L. a a Institute of Continuous Media Mechanics UB RAS, 1 Acad. Korolev St., Perm 614013, Russia XXIIth Winter School on Continuous Media Mechanics Indentation of soft material containing filler particles Izyumov R.I. a *, Sokolov A.K. a , Svistkov A.L. a a Institute of Continuous Media Mechanics UB RAS, 1 Acad. Korolev St., Perm 614013, Russia

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XXIIth Winter School on Continuous Media Mechanics” 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. © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review under responsibility of the scientific committee of the XXIIth Winter School on Continuous Media Mechanics” Keywords: Atomic-force microscopy; nanoindentation; filled nanocomposite; finite element modeling 1. Introduction At present, the continuous progress of atomic force microscopy (AFM) since its invention has made this method indispensable in many fields of science. The range of scientific areas includes studies of the structure, composition 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 nanofille . In exp r m ntal studies of materials using the nanoindentation mode of AFM, the in result is the curves describing the depende c of the cantilever bend on he probe penetration depth. The indentation can b carried o on a set of points on the mat rial surface and a map of the stiffness distribution can be obtained. The semi-contact mod is most often used in practice to study the eli f of an el stomeric nanocomposite. T obtain a correct interpretation f the data, the u e f mathematical models is requir d. An important lement of these models is the dep ndence of he elastic resistance force on the depth of the probe penetration into the material. The pap r p esents solutions to t problems of indentation of N o-Hookean material in the formulation of plane deformations. inclusion were prese ted as round particles. Solutions ar btained for th cases of indent near filler pa ticles of different sizes and with different depths of their location u der the surface. Computational experiments have shown that by the response to the probe indentation in o the material, we can obtain additional information (about the s ape and depth of inclusions), w ich can be used in the analysis of the mat rial structure data maps. © 2021 The Authors. Publi hed by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review u der re ponsibility of scientific committe of the XXIIth Winter School on Continuous Media Mechanics” K ywords: Atomic-force microscopy; nanoindentation; filled nanoc mposite; finite element modeling 1. Introduction At present, the continuous progress of atomic force microscopy (AFM) since its invention has made this method indispensable in many fields of sci nce. The range of scientific areas includes studies of he structure, compositi n 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.

* Corresponding author. Tel.: +7-982-257-8120. E-mail address: izumov@icmm.ru * Corresponding author. Tel.: +7-982-257-8120. E-mail address: izumov@icmm.ru

2452-3216 B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review under responsibility of the scientific committee of the XXIIth Winter School on Continuous Media Mechanics” B.V. This is an open access article under t CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4 0 ) Peer-review under responsibility of the scie tific committee of the XXIIth Winter School on Continuous Media Mechanics” © © 2021 2021 The The Authors. Authors. Published Published by by ELSEVIER ELSEVIER 2452-3216

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XXIIth Winter School on Continuous Media Mechanics” 10.1016/j.prostr.2021.09.013