Macroscopic out-of-plane auxetic features of a laminated open-cell structure with in-plane negative Poisson’s ratios induced by bridging beam components

Abstract

This paper presents the out-of-plane mechanism of a laminated open-cell structure that is exerted by a simple control of the geometric configuration. We propose two types of structural units that are assembled with beam and column members in a tetragonal system, and with the geometric difference between them being the presence of a reinforced beam. For the two unit cells, we develop finite element models according to a homogenization method and analyze the macroscopic linear and nonlinear elastic properties. The numerical results show that the cellular structure, which is bridged by additional beams, exhibits strong auxeticity with high negative values of Poisson’s ratio in the lamination direction, while retaining the in-plane negative Poisson’s ratios. We assess the sensitivity of the linear and nonlinear out-of-plane response to changes in the component geometry. Finally, we discuss the large deformation behaviors of the out-of-plane mechanisms to quantify the amounts of three-dimensional rotations of the internal components.

Conformational deformation of a multi-jointed elastic loop

“…Alternatively, no upper bound of G/E exists in continuum mechanics because G/E = 1/2(1 + ν) , where ν denotes the Poisson ratio and ν ∈ [−1, 1/2] for an isotropic material 31 . An elastic body with a large value of γ can potentially be developed using auxetic materials with negative Poisson ratios [31][32][33][34][35] . Considering a discrete system as an atomistic structure, the three potential energy functions given in terms of bond stretch, bond angle bending, and dihedral angle torsion are respectively equivalent in structural mechanics www.nature.com/scientificreports/ to the elastic strain energy of stretching, bending, and twisting under infinitesimal deformation 36 .…”

Auxetic vibration behaviours of periodic tetrahedral units with a shared edge

“…Various repetitive structures composed of simple geometric shapes have been investigated extensively with the endeavour to enhance fundamental properties such as rigidity and flexibility [1][2][3][4]. While many rigid microstructures based on trusses have been developed from a mechanical viewpoint [5,6], flexible microstructures are expected to realize anomalous mechanical characteristics in solid matter, being distinctive in having, for example, non-positive values of Poisson's ratio [7][8][9][10][11] or coefficient of thermal expansion [12][13][14].…”