Finite indentation of highly curved elastic shells

Area of Science:

• Biomechanics
• Materials Science
• Biophysics

Background:

• Measuring elastic properties of thin biological surfaces, especially curved ones, is difficult.
• Indentation experiments can determine fracture strength and elastic properties via force-displacement curves and mathematical models.
• Previous models assumed flat surfaces or failed for highly curved biological membranes due to wrinkling.

Purpose of the Study:

• To develop a new mathematical model for indenting curved biological membranes that accounts for bending stiffness.
• To enable accurate estimation of elastic properties for highly curved biological surfaces.

Main Methods:

• Developed a theoretical framework for indenting hyperelastic membranes with bending stiffness.
• Included previously neglected terms in the shell equilibrium equation.
• Utilized indentation experiments to validate the model.

Main Results:

• The new theory accurately models indentation of highly curved biological surfaces.
• Bending stiffness is crucial for accurate elastic property estimation in these systems.
• The model allows for shape- and size-independent elastic property determination.

Conclusions:

• This research provides a robust method for measuring the elastic properties of curved biological surfaces.
• The inclusion of bending stiffness significantly improves the accuracy of indentation-based biomechanical analysis.
• The findings are particularly relevant for understanding the mechanics of biological membranes.