Primitive rotation mechanism of periodic stellated octahedron units with sharing edges

Auxetic vibration behaviours of periodic tetrahedral units with a shared edge

“…In summary, we extended the periodic tetrahedral structure developed in our previous study [ 30 ] to the kinematic model in the free vibration problem. We revisit the geometrical framework with corner-to-corner and edge-to-edge sharing of tetrahedra and the bimode transformation characterized by the two types of edge-sharing tetrahedral motions.…”

“…The remaining vertices are connected pivotally with those in adjacent unit cells in an orthogonal periodic fashion. The periodic frameworks have over-constrained mechanisms with the states of self-stress and, assuming uniformity, a unit cell undergoes a continuous affine transformation having two degrees of freedom, here called the bimode transformation [ 30 ].…”

“…It seems that the depicted low-frequency behaviour with zero-stiffness is unstable in the linear vibration model. However, the bimode structure generates resistance like a solid under uniaxial finite transformation [ 30 ].…”

“…In our previous study, we proposed a class of constrained periodic polyhedral structures with two degrees of freedom and developed a static model involving interacting spring elements. Linear and nonlinear transformation analyses clarify why Poisson’s ratio of these structures is negative and undergoes a three-dimensional coordinated rotation of edge-shared tetrahedra [ 30 ]. Additionally, the structure exhibits zero stiffness at the initial configuration when the spring coefficients satisfy a specific condition.…”

Chiral two-dimensional periodic blocky materials with elastic interfaces: Auxetic and acoustic properties

“…Cellular flexible metamaterials have been proposed by Mizzi et al (2018) and Liang and Crosby (2020), who conceived two-dimensional plate-chain models of the periodic cell, namely chains of elastic or rigid polygonal plates connected at the vertices by flexible beams, to obtain strong auxeticity. Tridimensional rotating mechanisms have been recently proposed by Tanaka et al (2020) in which the unit cell is a stellated octahedron made up of tetrahedral units connected at the vertices with linear springs. Other auxetic materials have been proposed which are based on lattice structures defined by patterns of slits that follow chiral configurations.…”