Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices

TL;DR

This paper introduces a new continuum theory for 2D isotropic chiral solids that captures the chiral effect, which previous models could not adequately describe, and validates it through analysis and comparison with discrete models.

Contribution

A novel continuum model for 2D isotropic chiral solids incorporating a single chirality parameter, derived from homogenization of chiral lattices.

Findings

The model captures chiral effects not predicted by non-chiral theories.

Effective material constants for chiral lattices are analytically derived.

The model's predictions are validated against exact solutions of discrete models.

Abstract

In continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral. Therefore, influence of the chiral effect cannot be properly characterized by existing theories for 2D chiral solids. To circumvent this difficulty, based on reinterpretation of isotropic tensors in a 2D case, we propose a continuum theory to model the chiral effect for 2D isotropic chiral solids. A single material parameter related to chirality is introduced to characterize the coupling between the bulk deformation and the internal rotation which is a fundamental feature of 2D chiral solids. Coherently, the proposed continuum theory is also derived for a triangular chiral lattice from a homogenization procedure, from which the effective material constants of the lattice are analytically determined. The unique behavior in the chiral lattice is demonstrated through the analyses of a static tension problem and a plane wave propagation problem. The results, which cannot be predicted by the non-chiral model, are validated by the exact solution of the discrete model.