Compression of a pressurized spherical shell by a spherical or flat probe

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 45; no. 2; p. 13
• Main Authors: Couturier, Etienne, Vella, Dominic, Boudaoud, Arezki
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 14.02.2022; Springer Nature B.V; EDP Sciences: EPJ
• Subjects: Biological and Medical Physics; Biomechanical Phenomena; Biomechanics; Biophysics; Complex Fluids and Microfluidics; Complex Systems; Condensed Matter; Condensed matter physics; Contact pressure; Elastic Modulus; Elasticity; Indentation; Mechanical properties; Modulus of elasticity; Nanotechnology; Physics; Physics and Astronomy; Polymer Sciences; Pressure; Regular Article - Living Systems; Soft and Granular Matter; Soft Condensed Matter; Spherical shells; Surfaces and Interfaces; Thin Films; Tissue Mechanics
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/s10189-022-00166-6

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. Graphic Abstract