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. 2017 May 8;7:1541. doi: 10.1038/s41598-017-01784-3

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Validation of the developed algorithms with FE simulations. (a) Axisymmetric FE model, consisting of the rigid spherical indenter with 2 μm radius and viscoelastic sample with 15 μm height and radius. (b) Magnified view of the contact area, there the sample was meshed more finely. (c) Result of FE simulation and the F-δ curve modelled using Ting’s model with the same input parameters (SLS model with E ₀ = 2 kPa, E _∞ = 1 kPa, and τ = 0.1 s).