Interfacial metric mechanics: stitching patterns of shape change in active sheets

Area of Science:

• Soft Matter Physics
• Materials Science
• Geometric Mechanics

Background:

• Biological sheets exhibit metric mechanics through spontaneous shape change.
• Engineered soft matter sheets, like liquid crystal elastomers (LCEs), can mimic this behavior.
• Current methods lack a systematic approach to combine diverse shape-changing patterns.

Purpose of the Study:

• To develop a method for combining multiple programmed shape-changing patterns in a single sheet.
• To explore the geometric compatibility conditions for interfaces between different patterns.
• To investigate the resulting curvature and mechanical properties of stitched soft matter sheets.

Main Methods:

• Piecewise stitching of regions with distinct spontaneous shape-change patterns.
• Derivation of general conditions for geometric compatibility at interfaces.
• Analysis of interfaces in liquid crystal elastomers (LCEs) and swelling gels.

Main Results:

• Identified infinite and finite sets of compatible interfaces for discontinuous and continuous metrics, respectively, in LCEs.
• Demonstrated limited interface compatibility in isotropic systems like swelling gels.
• Showed that stitched interfaces generically develop singular Gaussian curvature, forming intrinsic folds.

Conclusions:

• Stitching distinct shape-changing patterns provides a versatile building-block approach for designing complex soft matter structures.
• The geometric compatibility conditions dictate the feasibility and type of interfaces achievable.
• Stitched interfaces possess unique geometric and mechanical properties, leading to predictable folding and curvature.