# Geometrically nonlinear Cosserat elasticity in the plane: applications to chirality

## TL;DR

This paper introduces a new intrinsically two-dimensional geometrically nonlinear Cosserat elasticity model for planar chiral materials, overcoming limitations of reduced three-dimensional theories and capturing additional nonlinear effects.

## Contribution

The authors develop a novel 2D Cosserat elasticity framework that models chiral materials without referencing higher dimensions, including nonlinear effects and plane wave solutions.

## Key findings

- Model aligns with existing equations of motion
- Includes additional nonlinear terms
- Brief discussion of plane wave solutions

## Abstract

Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to overcome this problem. We propose a new approach to this problem by formulating an intrinsically two-dimensional model which does not require references to a higher dimensional one. We are able to model planar chiral materials starting from a geometrically non-linear Cosserat type elasticity theory. Our results are in agreement with previously derived equations of motion but can contain additional terms due to our non-linear approach. Plane wave solutions are briefly discussed within this model.