Primitive rotation mechanism of periodic stellate d octahe dron units with sharing edges

摘要

The unique nonlinear mechanical properties including auxeticity of a class of orthotropic polyhedral structures are presented. These structures result from a three-dimensional coordinate rotation of the components. We establish an over-constrained periodic framework composed of edge-shared tetrahedra pivotally connected with each other. In the initial con?guration, the unit cell is a stellated octahedron and has two conformational mechanisms both subject to uniform transformations. Modeling the tetrahe-dral unit with linear spring interactions, the effective on-axis Poisson’s ratios and stress-strain curves are analyzed. In the restricted unimode model with a single degree of freedom under a uniaxial tension, the out-of-plane Poisson’s ratio is a negative constant determined only by the initial height ratio, whereas the in-plane Poisson’s ratio begins with-1 and slightly increases with increasing tension. The bimode model with additional geometric parameters exhibits a rich range of elastic behaviors, e.g., for any inter-nal stiffness, an identical point exists through which pass the equilibrium trajectories. The bimode model also displays similar auxetic characteristics to the unimode model.