https://doi.org/10.1140/epje/s10189-022-00166-6
Regular Article - Living Systems
Compression of a pressurized spherical shell by a spherical or flat probe
1
Laboratoire MSC, Université de Paris, 10 rue Alice Domon et Léonie Duquet, 75013, Paris, France
2
Mathematical Institute, University of Oxford, Woodstock Rd, OX2 6GG, Oxford, UK
3
LadHyX, CNRS, Ecole Polytechnique, IP Paris, 91128, Palaiseau Cedex, France
a
etienne.couturier@univ-paris-diderot.fr
Received:
19
November
2021
Accepted:
10
January
2022
Published online:
14
February
2022
Measuring the mechanical properties of cells and tissues often involves indentation with a sphere or compression between two plates. Different theoretical approaches have been developed to retrieve material parameters (e.g., elastic modulus) or state variables (e.g., pressure) from such experiments. Here, we extend previous theoretical work on indentation of a spherical pressurized shell by a point force to cover indentation by a spherical probe or a plate. We provide formulae that enable the modulus or pressure to be deduced from experimental results with realistic contact geometries, giving different results that are applicable depending on pressure level. We expect our results to be broadly useful when investigating biomechanics or mechanobiology of cells and tissues.
Guest editors: Alexandre Kabla, BenoÃRt Ladoux, Jean-Marc Di Meglio.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epje/s10189-022-00166-6.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022
