Primitive rotation mechanism of periodic stellated octahedron units with sharing edges

• Published in: International journal of solids and structures Vol. 185-186; pp. 485 - 499
• Main Authors: Tanaka, H., Suga, K., Shibutani, Y.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.03.2020; Elsevier BV
• Subjects: Auxeticity; Connecticity; Mechanical properties; Mechanisms; Nonlinear elastic behaviors; Poisson's ratio; Rotation; Stellated Octahedron; Stiffness; Strain analysis; Tetrahedra; Tetrahedral framework; Unit cell; Mechanisms; Auxeticity; Nonlinear elastic behaviors; Stellated Octahedron; Connecticity; Rotation; Tetrahedral framework
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2019.09.013

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 configuration, the unit cell is a stellated octahedron and has two conformational mechanisms both subject to uniform transformations. Modeling the tetrahedral 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 internal stiffness, an identical point exists through which pass the equilibrium trajectories. The bimode model also displays similar auxetic characteristics to the unimode model.