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

TL;DR

This paper extends theoretical models for indenting pressurized spherical shells with spherical or flat probes, providing formulas to determine mechanical properties from experimental data, aiding biomechanics research.

Contribution

It introduces new theoretical formulas for analyzing indentation of pressurized shells by spherical or flat probes, applicable to realistic contact geometries.

Findings

Formulas enable modulus or pressure estimation from indentation data.

Different results are provided depending on pressure levels.

Broad applicability in cell and tissue biomechanics.

Abstract

Measuring the mechanical properties of cells and tissues often involves indentation with a sphere, or compression between two plates. Previously, 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.