Curvature-Induced Instabilities of Shells

Area of Science:

• Mechanics of Materials
• Soft Matter Physics
• Biophysics

Background:

• Spontaneous curvature significantly impacts thin body morphology and mechanical stability.
• The interplay between spontaneous curvature and geometric frustration in curved shells is not well understood.

Purpose of the Study:

• To investigate the mechanical instabilities induced by spontaneous curvature in elastomeric spherical shells.
• To understand the role of geometric frustration in these instabilities.

Main Methods:

• Precision experiments on elastomeric spherical shells.
• Computational simulations.
• Theoretical modeling.

Main Results:

• Spontaneous curvature induces rotational symmetry-breaking buckling and Venus fly trap-like snapping instabilities.
• These instabilities depend on shell geometry.
• A novel effective mechanical load formulation (pressure-like bulk term, torque-like boundary term) accurately predicts instability scaling.

Conclusions:

• The effective mechanical load model provides a unified framework for understanding curvature-induced instabilities.
• The findings suggest curvature-induced subcritical buckling in closed shells.
• The results have broad applicability across various scales due to the prominent role of geometry.