A Comparison of Negative Compressibility between 3D Cellular Models Constructed by 2D Hinging Wine‐Rack and Hexagonal Honeycomb Mechanisms

Abstract

Herein, two kinds of 3D hexagonal honeycomb equivalent models are proposed, enlightened by the octahedron model constructed by the wine‐rack mechanism. They differ in their unit‐cell arrangement forms, which are array and homogeneous arrangements, respectively. Referring to the analysis of the octahedron model, the expressions of compressibility properties of the two new models are given and the conditions for obtaining negative compressibility are analyzed. Comparing these two models with the octahedron model, it is found that although the three models are quite different in externality, they have similar mechanical properties (Young's modulus, Poisson's ratio, and compressibility), and all have image symmetry in both horizontal directions. Further analysis shows that these three models are so unified that they can be expressed by a more general model, from which another model with negative compressibility can be deduced. Finally, a new method to improve negative compressibility property is concluded from comparing the three models, that is, increasing the number or length of rods without deformation in vertical direction can effectively improve negative compressibility property in this direction and weaken negative compressibility property in the other two directions.

Negative Compressibility in the Monoclinic Octahedron Model Constructed by Hinging Wine‐Rack Mechanism

“…Take a look at all three directions, it can be found that the NLC of the monoclinic octahedral model in three directions are not exactly the same, but they can simultaneously produce negative compressibility in any two directions under certain conditions. It is clearly different from the orthorhombic and tetragonal models studied previously, [ 3,33–35 ] which can simultaneously exhibit negative compressibility in the OX 1 and OX 2 directions for any conditions, and have a completely opposite angle range from the OX 3 direction. Figure 6a shows the conditions to obtain zero compressibility in the three directions, in which the red, blue, and green lines represent the model obtaining zero compressibility in the OX 1 , OX 2 , and OX 3 , respectively.…”

“…To better produce negative compressive deformation, the model should be set as idealized hinging model, but the bending and tensile deformation of rods cannot be avoided in practice. Therefore, as we previously set, [ 35 ] the joints between rods in this work are also connected through flexible hinge, which can enhance hinging deformation as much as possible and weaken bending and tensile deformation. The unit‐cell can be clearly shown in Figure 1b and the details of the flexure hinge can be observed in Figure 1c.…”

“…Referring to the analysis discussed in previous studies, [ 3,33–35 ] these linear compressibility can be used to obtain the expressions of the area compressibility and volume compressibility by the following formulas. The specific expressions are omitted here for the sake of simplification.…”

“…Zhou et al [ 33 ] constructed three different 3D analytical models based on the different layout of the 2D wine‐rack mechanism. Then Zhou et al [ 34,35 ] used the 2D hexagonal truss mechanism and wine‐rack mechanism to reconstruct some new 3D cellular models, which proved that in addition to the geometric parameters, the arrangement of framework, the layout orientations of 2D mechanism, and the number or length of rods without deformation in vertical direction can also change the extent of NLC and NAC. Arash Ghaedizadeh et al [ 1 ] designed two types of NLC composite structures, which proved that composite structures can be used to design NLC materials.…”

Negative Compressibility in Hexagonal and Trigonal Models Constructed by Hinging Wine‐Rack Mechanism

“…[21] Since Baughman et al [21] first proposed this property, it has gradually attracted widespread attention owing to its unconventional mechanical properties. Thus far, a large number of micromaterials [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] and macrostructures [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56] have been proved to exhibit negative compressibility. As for micromaterials, negative compressibility has been found to occur in a much greater variety of materials, ranging from molecular, [22,23] metal-organic frameworks (MOFs), [24,25] and polymers.…”