# Dimension reduction via Gamma-convergence for soft active materials

## TL;DR

This paper rigorously derives reduced-dimensional models for thin nematic elastomer sheets, capturing spontaneous bending and torsion, with focus on twist textures and their effects on curvature and bilayer configurations.

## Contribution

It introduces a mathematically rigorous derivation of 2D and 1D models for nematic elastomer sheets in the finite bending regime, focusing on twist textures and curvature effects.

## Key findings

- Derived 2D and 1D models for nematic elastomer sheets
- Analyzed effects of twist nematic textures on curvature
- Explored variants leading to different target curvatures

## Abstract

We present a rigorous derivation of dimensionally reduced theories for thin sheets of nematic elastomers, in the finite bending regime. Focusing on the case of twist nematic texture, we obtain 2D and 1D models for wide and narrow ribbons exhibiting spontaneous flexure and torsion. We also discuss some variants to the case of twist nematic texture, which lead to 2D models with different target curvature tensors. In particular, we analyse cases where the nematic texture leads to zero or positive Gaussian target curvature, and the case of bilayers.