Finite indentation of highly curved elastic shells. / Pearce, Simon; King, John; Steinbrecher, Tina; Leubner-Metzger, Gerhard; Everitt, Nicola; Holdsworth, Mike.

In: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol. 474, No. 2209, 01.2018, p. 1-18.

Research output: Contribution to journalArticlepeer-review

Published

Standard

Finite indentation of highly curved elastic shells. / Pearce, Simon; King, John; Steinbrecher, Tina; Leubner-Metzger, Gerhard; Everitt, Nicola; Holdsworth, Mike.

In: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol. 474, No. 2209, 01.2018, p. 1-18.

Research output: Contribution to journalArticlepeer-review

Harvard

Pearce, S, King, J, Steinbrecher, T, Leubner-Metzger, G, Everitt, N & Holdsworth, M 2018, 'Finite indentation of highly curved elastic shells', Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, vol. 474, no. 2209, pp. 1-18. https://doi.org/10.1098/rspa.2017.0482

APA

Pearce, S., King, J., Steinbrecher, T., Leubner-Metzger, G., Everitt, N., & Holdsworth, M. (2018). Finite indentation of highly curved elastic shells. Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, 474(2209), 1-18. https://doi.org/10.1098/rspa.2017.0482

Vancouver

Pearce S, King J, Steinbrecher T, Leubner-Metzger G, Everitt N, Holdsworth M. Finite indentation of highly curved elastic shells. Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences. 2018 Jan;474(2209):1-18. https://doi.org/10.1098/rspa.2017.0482

Author

Pearce, Simon ; King, John ; Steinbrecher, Tina ; Leubner-Metzger, Gerhard ; Everitt, Nicola ; Holdsworth, Mike. / Finite indentation of highly curved elastic shells. In: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences. 2018 ; Vol. 474, No. 2209. pp. 1-18.

BibTeX

@article{95da8a75199d4bd1be5b005be17f1016,
title = "Finite indentation of highly curved elastic shells",
abstract = "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, while 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 flat, 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.",
author = "Simon Pearce and John King and Tina Steinbrecher and Gerhard Leubner-Metzger and Nicola Everitt and Mike Holdsworth",
year = "2018",
month = jan,
doi = "10.1098/rspa.2017.0482",
language = "English",
volume = "474",
pages = "1--18",
journal = "Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences",
issn = "1471-2946",
publisher = "Royal Society",
number = "2209",

}

RIS

TY - JOUR

T1 - Finite indentation of highly curved elastic shells

AU - Pearce, Simon

AU - King, John

AU - Steinbrecher, Tina

AU - Leubner-Metzger, Gerhard

AU - Everitt, Nicola

AU - Holdsworth, Mike

PY - 2018/1

Y1 - 2018/1

N2 - 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, while 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 flat, 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.

AB - 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, while 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 flat, 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.

U2 - 10.1098/rspa.2017.0482

DO - 10.1098/rspa.2017.0482

M3 - Article

VL - 474

SP - 1

EP - 18

JO - Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences

SN - 1471-2946

IS - 2209

ER -