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Geometry of thin nematic elastomer sheets.

Hillel Aharoni¹, Eran Sharon¹, Raz Kupferman²

¹Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.

Physical Review Letters

|January 3, 2015

Summary

This summary is machine-generated.

Nematic elastomer sheets transform into 3D shapes when heated, controlled by their nematic director field. This study details their geometry and provides methods to engineer specific shapes and curvatures for advanced material applications.

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Area of Science:

Materials Science
Solid Mechanics
Soft Matter Physics

Background:

Nematic elastomers are stimuli-responsive materials that change shape with temperature.
The director field, representing molecular orientation, governs the elastomer's mechanical properties and shape transformations.
Understanding the relationship between director fields and resulting geometries is crucial for material design.

Purpose of the Study:

To describe the intrinsic geometry of thin nematic elastomer sheets.
To derive the metric induced by nematic director fields.
To investigate the reverse problem: constructing director fields for desired geometries and curvatures.

Main Methods:

Geometric analysis of thin nematic elastomer sheets.
Derivation of the induced metric based on director fields.
Development of a method to construct director fields for specified 2D geometries, including surfaces of revolution.
Analysis of director field gradients across the sheet's thickness to achieve hyperbolic reference curvature.

Main Results:

An expression for the metric induced by general nematic director fields was derived.
A method was established to construct director fields that induce specific 2D geometries.
Any surface of revolution can be explicitly constructed using this method.
A nontrivial hyperbolic reference curvature tensor was obtained by inscribing director field gradients.

Conclusions:

The intrinsic geometry of nematic elastomer sheets is dictated by the nematic director field.
Precise control over the 2D geometry of nematic elastomers can be achieved by designing director fields.
The ability to dictate actual configurations through reference metrics and curvature tensors opens possibilities for programmable soft materials.