# Study of In-Plane Mechanical Properties of Novel Ellipse-Based Chiral Honeycomb Structure
## 1 Introduction  
Negative Poisson's ratio (NPR) honeycomb structures refer to a class of man-made structural functional materials whose cross-sections become more expanded when stretched. Although scholars have previously discovered some natural materials with NPR effects, such as some metals [1], cancellous bones [2], cat skin [3] and parts of cow skin [4], the study on NPR materials started in the 1980s: [PERSON] et al. [5] systematically investigated the in-plane mechanical properties of hexagonal honeycomb structures with different parameters and found that re-entrant hexagonal honeycomb structures could produce the NPR effect; this result quickly attracted the attention of scholars, and different types of NPR structures were proposed, respectively. [PERSON] [6] designed a structure using rods, hinges and springs in two and three dimensions and found its Poisson's ratio to be \(-1\); [PERSON] [7] obtained a foam material with a Poisson's ratio of \(-0.7\) under compression in a heated mold using polyester foam as raw material and predicted the advantages and applications of NPR materials; [PERSON] et al. [8] designed NPR materials at the molecular level and named them Auxetics. As the research progresses, many unique and novel properties of NPR materials are gradually discovered, such as the varying porosity of NPR materials with strain [9; 10; 11] and isotropic curvature when subjected to out-plane bending [12; 13]. In addition, many mechanical properties of NPR materials are enhanced compared to those of ordinary materials, such as indentation resistance [14; 15; 16; 17; 18], shear modulus/fracture toughness [19; 20; 21; 22; 23] and energy absorption [24; 25; 26; 27]. Moreover, the properties of NPR materials are scale-independent and can be both the overall behavior of the material and originate from its internal structure, which means that they are both macroscopic material properties and microscopic internal structure properties [28]. Among many of the NPR honeycomb structures, chiral honeycomb structures have been widely studied due to their superior NPR effects and excellent designability. A typical chiral honeycomb structure usually consists of two parts, which are the central node and theligaments connected tangentially to the central node. Depending on the position and number of ligaments, chiral honeycomb structures can be classified into tri-trichiral honeycomb structure (tri)/anti-trichiral honeycomb structure (antitri), tetrachiral honeycomb structure (tet)/anti-tetrachiral honeycomb structure (antitet) and hexachiral honeycomb structure (hex), as shown in Figure 1. The NPR effect of chiral honeycomb structures originates from their unique deformation pattern, where the central node rotates when stressed in one direction and the ligaments connected to the central node bend, which leads to a kink in the whole structure and exhibits NPR effects. This unique deformation mode makes the chiral honeycomb structures have stable NPR over a wide range of strains. The study of chiral honeycomb structures by scholars began in the late 1980s: [PERSON] [29] first proposed that the NPR effect could be generated using rotating node topology; [PERSON] [30] proposed that chiral honeycomb structures can produce NPR effects; [PERSON] et al. [31] proposed hex and determined its parameters, basic theory and calculation methods to prove that the Poisson's ratio of hex is -1; [PERSON] et al. [32] investigated the in-plane mechanical properties of tri, antitri, tet, antitted and hex through theoretical derivations, finite element method (FEM) simulations and experiments and discussed the deformation mechanism of chiral honeycomb structures; [PERSON] et al. [33] investigated the out-plane mechanical properties of tri, antitri, tet, antitted and hex using theoretical derivations, FEM simulations and experiments; [PERSON] et al.