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

Area of Science:

• Biomechanics
• Mechanobiology
• Biophysics

Background:

• Cell and tissue mechanical properties are crucial for understanding biological functions.
• Indentation and compression are common experimental methods to measure these properties.
• Existing theoretical models often simplify contact geometries, limiting their applicability.

Purpose of the Study:

• To extend theoretical models for analyzing cell and tissue mechanics.
• To develop new formulae for deducing material parameters and state variables from indentation experiments.
• To account for realistic contact geometries, including spherical probes and plates.

Main Methods:

• Theoretical analysis of spherical pressurized shell indentation.
• Extension of point force indentation models to spherical probe and plate indentation.
• Derivation of formulae for calculating elastic modulus and pressure.

Main Results:

• New formulae are provided for deducing elastic modulus and pressure from experimental data.
• The formulae are applicable to realistic contact geometries (spherical probe, plate).
• Different results are obtained depending on the pressure level, offering more accurate analysis.

Conclusions:

• The developed formulae enhance the accuracy of mechanical property measurements in cells and tissues.
• These findings are broadly applicable to biomechanics and mechanobiology research.
• The study provides practical tools for investigating the mechanical behavior of biological materials.