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arXiv · 1203.4314

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

X. N. Liu·G. L. Huang·G. K. Hu
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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.

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X. N. Liu, G. L. Huang, G. K. Hu. 2012-03-20. Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices. https://doi.org/10.1016/j.jmps.2012.06.008

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