Geometrically controlled snapping transitions in shells with curved creases.

Area of Science:

• Materials Science
• Mechanical Engineering
• Geometry

Background:

• The mechanics of thin materials are intrinsically linked to their curvature.
• Folding principles for flat surfaces are established, but folding curved shells remains poorly understood.
• Shell deformation involves coupled bending and stretching, enhancing stability but complicating folding.

Purpose of the Study:

• To theoretically and experimentally investigate the folding mechanics of creased curved shells.
• To identify the geometric conditions governing smooth folding versus snapping transitions.
• To establish a design rule for creating programmable multistable materials with fast actuation.

Main Methods:

• Theoretical analysis of shell folding geometry.
• Experimental validation of folding behaviors.
• Computational simulations of shell deformation.

Main Results:

• Geometric conditions for smooth folding of creased shells were theoretically derived.
• Violation of these conditions leads to rapid snapping transitions between stable states.
• Shell geometry, specifically creases and curvature, inherently drives snapping, independent of material asymmetry.

Conclusions:

• The inherent geometry of creased shells, not material properties, governs folding dynamics.
• A novel design rule based on creases and curvature enables predictable snapping transitions.
• This facilitates the development of programmable multistable materials with rapid actuation capabilities.