Curvature-driven morphing of non-Euclidean shells

Area of Science:

• * Solid Mechanics
• * Geometric Mechanics
• * Materials Science

Background:

• * Understanding how thin structures respond to non-mechanical stimuli is crucial for designing advanced materials and devices.
• * Existing models often struggle to capture complex shape changes driven by variations in natural curvature.

Purpose of the Study:

• * To develop an effective geometric model for predicting shape changes in thin structures under non-mechanical stimuli.
• * To investigate the relationship between a structure's natural curvature and its deformation response.
• * To validate the model's predictions against numerical simulations for various geometries.

Main Methods:

• * Derivation of an effective model based on the theory of non-Euclidean plates and shells.
• * Incorporation of thickness expansion (growth) into the model.
• * Application and numerical validation of the model to diverse thin bodies (plates, shells, cylinders, cones).

Main Results:

• * Excellent agreement between theoretical predictions and numerical simulations was achieved.
• * Demonstrated that cylinders and cones can exhibit bending, unrolling, snapping, and rotation.
• * Characterized nearly isometric deformations of spherical shells using spindle geometry.

Conclusions:

• * The derived geometric model provides a general and scalable framework for predicting shape changes in thin structures.
• * The findings offer insights into the fundamental mechanisms governing structure deformation in response to curvature variations.
• * The model's purely geometrical basis ensures broad applicability across different materials and scales.