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Indentation of ellipsoidal and cylindrical elastic shells
Dominic Vella1, Amin Ajdari, Ashkan Vaziri
1OCCAM, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, United Kingdom.
Physical Review Letters
|October 23, 2012
Summary
The stiffness of thin elastic shells, crucial for their function, depends on their geometry and internal pressure. This study reveals how shell curvature dictates rigidity, impacting natural structures from viruses to eggs.
Area of Science:
- Physics
- Materials Science
- Biophysics
Background:
- Thin shells are ubiquitous in nature, from viruses to eggs.
- Shell stiffness is critical for the function of these biological and synthetic structures.
Purpose of the Study:
- To investigate the indentation mechanics of ellipsoidal and cylindrical elastic shells.
- To provide a theoretical basis for experimental findings on shell indentation and turgor pressure inference.
Main Methods:
- Numerical simulations of shell indentation.
- Theoretical analysis of elastic shell mechanics.
- Consideration of both pressurized and unpressurized shell conditions.
Main Results:
- Indentation stiffness is governed by shell curvature (mean or Gaussian).
- The dominant curvature depends on pressurization and indentation depth.
- A new indentation regime was identified for large indentations.
Conclusions:
- Shell geometry fundamentally rules the rigidity of thin elastic shells.
- The findings support experimental studies on shell mechanics and turgor pressure.
- Understanding these principles is key for diverse applications involving thin shells.
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