Micropolar Modeling of Auxetic Chiral Lattices With Tunable Internal Rotation

Abstract

Based on micropolar continuum theory, the closed-form stiffness tensor of auxetic chiral lattices with V-shaped wings and rotational joints were derived. Representative volume element (RVE) of the chiral lattice was decomposed into V-shape wings with fourfold symmetry. A unified V-beam finite element was developed to reduce the nodal degrees of freedoms of the RVE to enable closed-form analytical solutions. The elasticity constants were derived as functions of the angle of the V-shaped wings, nondimensional in-plane thickness of the ribs, and the stiffness of the rotational joints. The influences of these parameters on the coupled chiral and auxetic effects were systematically explored. The results show that the elastic moduli were significantly influenced by all three parameters, while Poisson's ratio was barely influenced by the in-plane thickness of the ribs but is sensitive to the angle of the V-shaped wings and the stiffness of the rotational springs. There is a transition region out of which the spring stiffness does not considerably affect the auxeticity and the overall lattice stiffness.