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

Abstract

a b s t r a c tIn 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.

Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial

“…The wave mechanism of the EMM with chiral microstructure was interpreted and can be found in ref. 31.…”

“…2a. The difference can be attributed to the strong anisotropy of the current microstructural design, which cannot be exactly captured by using the effective isotropic medium 31 . For the chiral topology, the number of the chirally distributed ribs, N r , is an important parameter for the global property of the EMM with chiral microstructure.…”

A New Chiral Beam Element for Modelling Chiral Honeycombs

“…The nodes may be hollow or solid in the real cases, but in this paper, they are assumed rigid while only the ligament (treated as a slender beam) is considered as deformable [1,14,16,21]. With this assumption, the nodes may be replaced by the material points (B and D in Figure 2) whose translational and rotational motions are related to the elastic ligament.…”

Modeling of micropolar type chiral structures

“…Одним из примеров таких свойств является свойство ауксетичности, то есть свойство материала расширяться в поперечном направ-лении при его растяжении. Все более активно обсужда-ются вопросы моделирования, особенности поведения хиральных структур, возможности их практического применения [1][2][3]. Настоящая статья представляет обо-бщение известных результатов и некоторые новые ре-зультаты исследований авторов в этом направлении.…”