1. Introduction
Under uniaxial tensile loads, conventional materials usually experience a decrease in their cross-sectional area perpendicular to the direction of the applied load, demonstrating positive Poisson’s ratio behavior. Negative Poisson’s ratio materials demonstrate a unique behavior when subjected to uniaxial tensile loads, expanding in the direction perpendicular to the applied force. This phenomenon is commonly known as the negative Poisson’s ratio effect [
1]. This unique tensile expansion behavior makes the negative Poisson’s ratio have the advantages of being light weight and having high shear modulus, excellent impact resistance, good energy absorption and vibration, and noise reduction capabilities [
2], and it has broad application prospects in many fields [
3]. In aerospace engineering, Poisson’s ratio can be used to design metamaterials as in-orbit satellite launch surface materials, which can improve the deformation ability of in-orbit satellite antenna reflective surface reconstruction processes, reduce local stress and actuation force, and improve the accuracy of surface reconstruction [
4]. In biomedical engineering, the use of 2D negative Poisson’s ratio materials to make auxiliary tubular structures can significantly increase the oxygen-aiding function of oxygen-enhancing tube structures [
5]. Chen et al. [
6] investigated the effect of negative Poisson’s ratio bolts on rock reinforcement using RFPA software. The experimental results proved that the negative Poisson’s ratio anchor can significantly improve the bearing capacity of anchored rock and absorb more energy. Wu et al. [
7] proposed a double concave lens-shaped structure with a large value of negative Poisson’s ratio (LNPR) and designed a new vibration isolator with frequency-dependent damping characteristics. The negative Poisson’s ratio structure has evolved and developed into a concave-angle structure [
8,
9,
10], a chiral structure [
11], a rotating rigid body structure [
12], a perforated plate structure [
13], a pleated structure [
14], and other structural forms. The concave angle structure can be divided into an arrow [
9], a hexagon [
8], and a star [
10] according to the number.
The deformation characteristics and mechanical properties of honeycomb structures under loads such as tensile, bending, and torsion are also hot topics of research. Li et al. [
15] demonstrated through static dynamic experimental tests that negative Poisson’s ratio composites have higher indentation stiffness and impact resistance compared with ordinary composites. Tho et al. [
16] used the third-order shear deformation theory combined with the phase field theory to investigate core layer fracture only. The free vibration response and static bending of laminated composite plates with only core fracture were modeled. Zhang et al. [
17] investigated the dynamic response of honeycomb sandwich panels under different loads, such as step load, wind-burst load, sinusoidal load, triangular load, and incremental load and verified the excellent mechanical properties of the negative Poisson’s ratio material. Based on finite element analysis, Zhu et al. [
18] developed a novel reinforced six-arm missing pillar chiral tensile expansion metamaterial with an adjustable constant negative Poisson’s ratio in a large deformation range, revealing the microstructure–mechanical property relationship. However, the conventional negative Poisson’s ratio honeycomb is mostly a two-dimensional structure and less studied for three dimensions [
19]. This traditional two-dimensional honeycomb model exhibits a negative Poisson’s ratio effect when loaded in-plane but does not show the pulling and swelling effect when loaded out-of-plane [
20]. The research on negative Poisson’s ratio materials is still focused on theoretical studies and is limited in application.
Three-dimensional printing technology has matured and introduced new design dimensions, enriching the diversity of structural design and making negative Poisson’s ratio structures with more excellent properties. Jiang et al. [
21] used 3D printing technology to print a modified “Buckley crystal assisted structure” and demonstrated the ability of this new implant to contract laterally under compression, which can be used to relieve lumbar disc herniation. Kim et al. [
22] developed new soft-assisted structures with the help of 3D printing technology to achieve high manufacturing reliability and repeatability. Xue et al. [
23] investigated the properties of negative Poisson’s ratio and folded hexagonal honeycomb structures through light-curing 3D printing experiments.
To this end, this paper proposes a three-dimensional negative Poisson’s ratio cell and a corresponding composite structure based on a two-dimensional star-shaped negative Poisson’s ratio cell. This structure has negative Poisson’s ratio properties in all three main directions and is lighter than the two-dimensional structure. With the improvement in processing and the preparation process, it will also have a broader application prospect. The authors firstly used the finite element method to simulate the star-shaped negative Poisson’s ratio structure numerically, then carried out a model compression test with the help of 3D printing technology, and finally studied the influence of the structural form and material properties on the mechanical characteristics of the 3D star-shaped negative Poisson’s ratio composite structure through a parametric analysis system.
4. Conclusions
Based on an octagonal two-dimensional negative Poisson’s cell, a three-dimensional star-shaped negative Poisson’s cell and a three-dimensional star-shaped negative Poisson’s composite structure are proposed. Through numerical simulation, model test, and parameter analysis, the mechanical characteristics of a three-dimensional star-shaped negative Poisson composite structure are discussed:
(1) The negative Poisson’s ratio effect and hyperbolic properties of the three-dimensional star-shaped negative Poisson’s ratio cytomatrix and three-dimensional star-shaped negative Poisson’s composite structure were verified, and the analysis showed that the equivalent Poisson’s ratio of the cytomatrix and the composite structure differed by 4.1%, The difference in the equivalent elastic modulus is 3.1%, which indicates that the cytogenic analysis can reflect the mechanical characteristics of the composite structure to a certain extent.
(2) The experimental values of the equivalent elastic modulus are similar to the finite element calculation results, which verifies the correctness of the model and proves that the newly designed 3D star-shaped negative Poisson’s ratio cell element and composite structure have a good negative Poisson’s effect.
(3) Parametric analysis shows that: the main factor affecting the equivalent Poisson’s ratio and equivalent elastic modulus of the structure is the form of the structure; the equivalent elastic modulus is proportional to t and inversely proportional to θ; the Poisson’s ratio approaches 0 as the angle of θ increases; the equivalent elastic modulus is positively correlated with the material Poisson’s ratio and the equivalent elastic modulus increases by 1.5% for every 0.05 increase in the material Poisson’s ratio.
(4) For eight different real materials, the negative Poisson’s ratio effect does not vary much, with the effect for all of them being between −0.058 to −0.050. The best effect is for rubber. For metallic materials, the effect of the copper alloy is relatively the best.