Du, Y. , Stewart, P. , Hill, N. A. , Yin, H. , Penta, R. , Köry, J. , Luo, X. and Ogden, R. (2023) Nonlinear indentation of second-order hyperelastic materials. Journal of the Mechanics and Physics of Solids, 171, 105139. (doi: 10.1016/j.jmps.2022.105139)
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Abstract
The classical problem of indentation on an elastic substrate has found new applications in the field of the Atomic Force Microscopy. However, linearly elastic indentation models are not sufficiently accurate to predict the force–displacement relationship at large indentation depths. For hyperelastic materials, such as soft polymers and biomaterials, a nonlinear indentation model is needed. In this paper, we use second-order elasticity theory to capture larger amplitude deformations and material nonlinearity. We provide a general solution for the contact problem for deformations that are second-order in indentation amplitude with arbitrary indenter profiles. Moreover, we derive analytical solutions by using either parabolic or quartic surfaces to mimic a spherical indenter. The analytical prediction for a quartic surface agrees well with finite element simulations using a spherical indenter for indentation depths on the order of the indenter radius. In particular, the relative error between the two approaches is less than 1% for an indentation depth equal to the indenter radius, an order of magnitude less than that observed with models which are either first-order in indentation amplitude or those which are second-order in indentation amplitude but with a parabolic indenter profile.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Yin, Professor Huabing and Ogden, Professor Raymond and Penta, Dr Raimondo and Luo, Professor Xiaoyu and Stewart, Professor Peter and Du, Dr Yangkun and Hill, Professor Nicholas and Koery, Dr Jakub |
| Authors: | Du, Y., Stewart, P., Hill, N. A., Yin, H., Penta, R., Köry, J., Luo, X., and Ogden, R. |
| College/School: | College of Science and Engineering > School of Engineering > Biomedical Engineering College of Science and Engineering > School of Mathematics and Statistics College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of the Mechanics and Physics of Solids |
| Publisher: | Elsevier |
| ISSN: | 0022-5096 |
| ISSN (Online): | 1873-4782 |
| Published Online: | 20 November 2022 |
| Copyright Holders: | Copyright © 2022 The Authors |
| First Published: | First published in Journal of the Mechanics and Physics of Solids 171: 105139 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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