Static bistability of spherical caps.

Area of Science:

• Mechanical Engineering
• Materials Science
• Physics of Soft Matter

Background:

• Spherical shells exhibit bistability, existing in two stable configurations without external force, like an umbrella or contact lens.
• The exact geometric conditions for spherical shell bistability remain largely undefined.
• Understanding bistability is crucial for designing structures with tunable mechanical properties.

Purpose of the Study:

• To experimentally and computationally determine the geometric threshold for bistability in spherical shells.
• To assess the validity of shallow shell theory in predicting bistability for various shell depths.
• To investigate the impact of pointwise indentation on the stability and transition between bistable states.

Main Methods:

• Conducting physical experiments with spherical shells of varying solid angles.
• Employing finite-element simulations to model shell behavior.
• Comparing experimental results with predictions from modified shallow shell theory.

Main Results:

• Established the critical solid angle threshold that distinguishes bistable from monostable spherical shells.
• Demonstrated that modified shallow shell theory accurately predicts bistability even for deep shells.
• Found that indentation facilitates state transitions in near-threshold shells, but induces asymmetric buckling in thinner shells, enhancing their robustness.

Conclusions:

• Precisely defined the geometric parameters governing spherical shell bistability.
• Validated and refined shallow shell theory for predicting bistable behavior.
• Characterized the complex influence of indentation on shell stability, revealing mechanisms for enhanced robustness and asymmetric buckling.