Elasto-static micropolar behavior of a chiral auxetic lattice

Abstract

a b s t r a c tAuxetic materials expand when stretched, and shrink when compressed. This is the result of a negative Poisson's ratio n. Isotropic configurations with n % À1 have been designed and are expected to provide increased shear stiffness G. This assumes that Young's modulus and n can be engineered independently. In this article, a micropolarcontinuum model is employed to describe the behavior of a representative auxetic structural network, the chiral lattice, in an attempt to remove the indeterminacy in its constitutive law resulting from n ¼ À1. While this indeterminacy is successfully removed, it is found that the shear modulus is an independent parameter and, for certain configurations, it is equal to that of the triangular lattice. This is remarkable as the chiral lattice is subject to bending deformation of its internal members, and thus is more compliant than the triangular lattice which is stretch dominated. The derived micropolar model also indicates that this unique lattice has the highest characteristic length scale l c of all known lattice topologies, as well as a negative first Lamé constant without violating bounds required for thermodynamic stability. We also find that hexagonal arrangements of deformable rings have a coupling number N ¼1. This is the first lattice reported in the literature for which couple-stress or Mindlin theory is necessary rather than being adopted a priori.

Low Porosity Metallic Periodic Structures with Negative Poisson's Ratio

“…In all of these cases, careful design of the microstructure has lead to effective Poisson's ratios ν < 0, despite the fact that the bulk materials are characterized by ν > 0. In particular, it has been shown that auxetic behavior can be achieved in a variety of highly porous materials [10], including foams with re-entrant [11][12][13][14][15] and chiral [16,17] microstructure, microporous polymeric materials [18], networks of rigid units [19] and skeletal structures [20]. Moreover, negative Poisson's ratio has also been shown in non-porous systems, such as laminates [21,22], sheets assemblies of carbon nanotubes [23], composites [24] and polycrystalline thin films [25].…”

Modeling of micropolar type chiral structures

“…Перемещения и вращения внутренних узлов трехзвенного соединения однозначно выражаются че-рез перемещения и вращения крайних узлов. Исключив внутренние степени свободы, после преобразований вы-ражение потенциала соединения может быть записано в виде (1). Выражения для параметров потенциала (1) че-рез параметры балочных элементов трехзвенного соеди-нения (рис.…”

“…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.…”

Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

“…The mechanical behavior of chiral materials is of interest for the investigation of carbon nanotubes (Chandraseker and Mukherjee, 2006;Guz et al, 2007, Chandraseker et el., 2009, auxetic materials (Lakes, 1991(Lakes, , 1998Prall and Lakes, 1997;Spadoni and Ruzzene, 2012) and bones (Lakes et al, 1983;Park and Lakes, 1986). It is known that the deformation of chiral elastic materials cannot be described within classical elasticity.…”