Ridge energy for thin nematic polymer networks

TL;DR

This paper extends the theory of thin nematic polymer networks by including ridged isometric immersions, modeling the energy along sharp ridges, and predicting fold patterns based on material order and external stimuli.

Contribution

It introduces a new model for energy along ridges in nematic polymer networks, broadening the class of admissible deformations beyond smooth isometric immersions.

Findings

Energy along ridges scales quadratically with thickness under certain conditions.

The model predicts the number of folds based on the induced order in the material.

Application to a disk with a radial hedgehog shows how external stimuli influence folding patterns.

Abstract

Minimizing the elastic free energy of a thin sheet of nematic polymer network among smooth isometric immersions is the strategy purported by the mainstream theory. In this paper, we broaden the class of admissible spontaneous deformations: we consider ridged isometric immersions, which can cause a sharp ridge in the immersed surfaces. We propose a model to compute the extra energy distributed along such ridges. This energy comes from bending; it is shown under what circumstances it scales quadratically with the sheet's thickness, falling just in between stretching and bending energies. We put our theory to the test by studying the spontaneous deformation of a disk on which a radial hedgehog was imprinted at the time of crosslinking. We predict the number of folds that develop in terms of the degree of order induced in the material by external agents (such as heat and illumination).