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Anisotropic blistering instability of highly ellipsoidal shells
Hamid Ebrahimi1, Amin Ajdari2, Dominic Vella3
1Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA.
Physical Review Letters
|March 25, 2014
Summary
Highly ellipsoidal shells exhibit a novel "blistering" instability when indented. This phenomenon, unlike spherical shell crushing, forms blisters along the long axis and can determine shell thickness.
Area of Science:
- Solid Mechanics
- Materials Science
- Applied Physics
Background:
- Localized periodic structures are common in the deformation of elastic shells, notably in the crushing of spherical shells like ping-pong balls, which form polygonal patterns.
- The behavior of ellipsoidal shells under indentation, particularly the onset of new instabilities, is less understood compared to spherical counterparts.
Purpose of the Study:
- To investigate and characterize a novel instability observed during the indentation of highly ellipsoidal elastic shells.
- To explain the mechanism behind this new instability using theoretical and experimental approaches.
- To determine the factors influencing the properties of the observed instability pattern.
Main Methods:
- Experimental indentation of highly ellipsoidal elastic shells with a horizontal plate.
- Development of scaling arguments to theoretically describe the instability.
- Numerical simulations to model the shell deformation and instability onset.
- Characterization of the blistering pattern's dependence on shell geometry and indentation depth.
Main Results:
- A new instability, termed 'blistering', was observed in ellipsoidal shells above a critical indentation depth, where the indenter loses contact along the long axis.
- The number and size of blisters depend on shell geometry and indentation depth, but notably not on the shell's elastic modulus.
- Scaling arguments, numerical simulations, and experiments consistently explain the onset and characteristics of this blistering instability.
Conclusions:
- The study identifies and explains a unique blistering instability in indented ellipsoidal shells, distinct from the polygonal structures seen in spherical shells.
- The findings provide a method for determining the thickness of highly ellipsoidal shells by analyzing their blistering response under indentation.
- This research advances the understanding of thin shell mechanics and offers a practical application in material characterization.
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