Finite indentation of highly curved elastic shells
Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, whilst measuring the applied force and displacement. This gives immediate...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Published: |
Royal Society
2018
|
| Online Access: | https://eprints.nottingham.ac.uk/48804/ |
| _version_ | 1848797851783528448 |
|---|---|
| author | Pearce, Simon P. King, John R. Steinbrecher, Tina Leubner-Metzger, Gerhard Everitt, Nicola M. Holdsworth, Michael J. |
| author_facet | Pearce, Simon P. King, John R. Steinbrecher, Tina Leubner-Metzger, Gerhard Everitt, Nicola M. Holdsworth, Michael J. |
| author_sort | Pearce, Simon P. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, whilst measuring the applied force and displacement. This gives immediate information on the fracture strength of the material (from the force required to puncture), but it is also theoretically possible to determine the elastic properties by comparing the resulting force-displacement curves with a mathematical model. Existing mathematical studies generally assume that the elastic surface is initially at, which is often not the case for biological membranes. We previously outlined a theory for the indentation of curved isotropic, incompressible, hyperelastic membranes (with no bending stiffness) which breaks down for highly curved surfaces, as the entire membrane becomes wrinkled. Here we introduce the effect of bending stiffness, ensuring that energy is required to change the shell shape without stretching, and find that commonly neglected terms in the shell equilibrium equation must be included. The theory presented here allows for the estimation of shape- and size-independent elastic properties of highly curved surfaces via indentation experiments, and is particularly relevant for biological surfaces. |
| first_indexed | 2025-11-14T20:10:27Z |
| format | Article |
| id | nottingham-48804 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:10:27Z |
| publishDate | 2018 |
| publisher | Royal Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-488042020-05-04T19:28:14Z https://eprints.nottingham.ac.uk/48804/ Finite indentation of highly curved elastic shells Pearce, Simon P. King, John R. Steinbrecher, Tina Leubner-Metzger, Gerhard Everitt, Nicola M. Holdsworth, Michael J. Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, whilst measuring the applied force and displacement. This gives immediate information on the fracture strength of the material (from the force required to puncture), but it is also theoretically possible to determine the elastic properties by comparing the resulting force-displacement curves with a mathematical model. Existing mathematical studies generally assume that the elastic surface is initially at, which is often not the case for biological membranes. We previously outlined a theory for the indentation of curved isotropic, incompressible, hyperelastic membranes (with no bending stiffness) which breaks down for highly curved surfaces, as the entire membrane becomes wrinkled. Here we introduce the effect of bending stiffness, ensuring that energy is required to change the shell shape without stretching, and find that commonly neglected terms in the shell equilibrium equation must be included. The theory presented here allows for the estimation of shape- and size-independent elastic properties of highly curved surfaces via indentation experiments, and is particularly relevant for biological surfaces. Royal Society 2018-01-24 Article PeerReviewed Pearce, Simon P., King, John R., Steinbrecher, Tina, Leubner-Metzger, Gerhard, Everitt, Nicola M. and Holdsworth, Michael J. (2018) Finite indentation of highly curved elastic shells. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2209). pp. 1-17. ISSN 1471-2946 http://rspa.royalsocietypublishing.org/content/474/2209/20170482 doi:10.1098/rspa.2017.0482 doi:10.1098/rspa.2017.0482 |
| spellingShingle | Pearce, Simon P. King, John R. Steinbrecher, Tina Leubner-Metzger, Gerhard Everitt, Nicola M. Holdsworth, Michael J. Finite indentation of highly curved elastic shells |
| title | Finite indentation of highly curved elastic shells |
| title_full | Finite indentation of highly curved elastic shells |
| title_fullStr | Finite indentation of highly curved elastic shells |
| title_full_unstemmed | Finite indentation of highly curved elastic shells |
| title_short | Finite indentation of highly curved elastic shells |
| title_sort | finite indentation of highly curved elastic shells |
| url | https://eprints.nottingham.ac.uk/48804/ https://eprints.nottingham.ac.uk/48804/ https://eprints.nottingham.ac.uk/48804/ |