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

By Xiaoning Liu, Guoliang Huang, G. Hu. 2012

213 citations recorded by the source corpus.

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 the 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 applied for the homogenization of a triangular chiral lattice, 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 verified by the exact solution of the discrete model.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6473e8b7bb17eefa86d24a471ae7df2ee66bff9f

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Modulated phononic crystals: Non-reciprocal wave propagation and Willis materials (2017, background): “Systems of the first class qualify as intrinsic and involve using structural chirality, dissipation and non-linearity ( Liang et al., 2009; Liu et al., 2011, 2012; Mousavi et al., 2015 ).”
Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, background): “Non-standard elastodynamics properties such as, for instance, the cloaking effect, are at the very beginning of the studies of what is presently known as metamaterials [43,47,41].”
Controllable thermal expansion of large magnitude in chiral negative Poisson's ratio lattices (2015, methodology): “Chiral lattices have been analyzed [10] in the context of Cosserat (micropolar) elasticity [11] in which rotation of points has physical significance.”
Homogenization of periodic hexa- and tetrachiral cellular solids (2014, methodology): “For hexachiral cells, the solution of Liu et al., 2012, is found, showing the auxetic property of the lattice together with the elastic coupling modulus between the normal and the asymmetric strains; a property that has been confirmed here for the tetrachiral lattice.”
Chiral three‐dimensional isotropic lattices with negative Poisson's ratio (2016, unknown): “Chiral 2D lattices [2] have been analyzed [23, 24] in the context of Cosserat elasticity.”