A ribbon model for nematic polymer networks

TL;DR

This paper develops a theoretical model for the deformation behavior of nematic polymer network ribbons, deriving a reduced energy functional and demonstrating complex shape changes upon activation.

Contribution

It introduces a dimension reduction approach to derive a ribbon energy from a nematic elastomer sheet model, enabling analysis of ribbon deformations.

Findings

Derived a 2D energy for NPN ribbons from 3D sheet energy.

Showed a rectangular NPN ribbon can undergo serpentine deformations.

Provided an illustrative example of shape change upon activation.

Abstract

We present a theory of deformation of ribbons made of nematic polymer networks (NPNs). These materials exhibit properties of rubber and nematic liquid crystals, and can be activated by external stimuli of heat and light. A two-dimensional energy for a sheet of such a material has already been derived from the celebrated neo-classical energy of nematic elastomers in three space dimensions. Here, we use a dimension reduction method to obtain the appropriate energy for a ribbon from the aforementioned sheet energy. We also present an illustrative example of a rectangular NPN ribbon that undergoes in-plane serpentine deformations upon activation under an appropriate set of boundary conditions.