Curvature-driven instabilities in thin active shells.

Area of Science:

• Physics
• Materials Science
• Mechanical Engineering

Background:

• Spontaneous material shape changes (e.g., swelling, thermal expansion) can induce significant elastic instabilities in thin shells.
• These instabilities arise from geometric incompatibility between a shell's preferred extrinsic and intrinsic curvatures.
• Active deformations, through or in plane, can modify these curvatures.

Purpose of the Study:

• To analyze the simplest model of elastic instabilities in shallow, thin shells.
• To investigate instabilities under homogeneous preferred curvatures for zero, positive, and negative Gauss curvature cases.
• To characterize symmetry-breaking, inversion, and rotation instabilities.

Main Methods:

• Solving a simplified elastic instability model for shallow shells.
• Analyzing shells that bend but do not stretch.
• Considering shells with homogeneous preferred curvatures.

Main Results:

• Identified two types of supercritical symmetry-breaking instabilities (discrete up/down and continuous planar isotropy).
• Observed subcritical inversion instabilities and energy-free rotation instabilities.
• Determined thickness-independent thresholds for preferred extrinsic curvature, proportional to the square root of Gauss curvature.

Conclusions:

• The study provides a fundamental understanding of elastic instabilities in thin shells driven by material shape changes.
• The identified instabilities and their thresholds offer insights into shell behavior under geometric constraints.
• Results align with experimental data for deep spherical caps, validating the model.