# Negative Poisson's Ratio Lattice Structure with Chiral and Re-Entrant Properties
## 1 Introduction
Additionally, a multi-material chiral mechanical metamaterial exhibiting the most optimal negative Poisson's ratio and stiffness was synthesized through the integration of a point-wise smart interpolation model and a bimaterial interpolation method [54]. Furthermore, the advancement of 3D printing technology has opened up new avenues for the production of three-dimensional chiral materials. [PERSON] et al. [55] introduced structures exhibiting a significant negative Poisson's ratio effect when subjected to large deformation conditions through the utilization of multi-material 3D printing technology. [PERSON] et al. [56] have also proposed the fabrication of star-shaped perforated chiral metamaterials using 3D printing technology. The investigation of re-entrant structures primarily centers around the dynamics of impact, which can be ascribed to the symmetry and lattice properties inherent in these structures. These characteristics render re-entrant structures more efficient in withstanding impact forces. [PERSON] et al. [7] introduced a novel foam-filled two-dimensional negative Poisson's ratio concave hexagonal honeycomb structure that exhibits a high specific energy absorption capacity. [PERSON] et al. [57] successfully enhanced the rigidity of a stretch-dominated lattice by incorporating reinforcing ribs that were oriented perpendicular to the concave direction within conventional stretching unit cells. [PERSON] [58] conducted an investigation on the properties of negative thermal expansion in concave triangular cell structures made from two distinct materials, highlighting their potential advantages in the field of composite materials. [PERSON] [59] conducted a comprehensive investigation into the alterations in negative Poisson's ratio observed in honeycomb structure materials when subjected to dynamic compression conditions. Inspired by the architectural design of ancient Chinese window grills, we have proposed a lattice structure that integrates both chirality and re-entrant characteristics. The structures investigated in this paper pertain to the anti-four-fold chiral class of structures, and there exists a multitude of structures that fall within this classification. For instance, [PERSON] [60] conducted an investigation on the influence of disorder in anti-chiral rectangular structures using the finite element method (FEM). [PERSON] [61] conducted a study on the significant deformations of a structure that bears resemblance to those discussed in this paper, utilizing the finite element method (FEM). [PERSON] [62] conducted a comprehensive analysis to investigate anti-tetra-chiral structures. There have been studies conducted on the molecular level regarding tetra-chiral auxetic systems that exhibit similarities [63; 64; 65]. Furthermore, [PERSON] conducted a comprehensive investigation into different auxetic structures that are derived from ancient geometrical patterns [66; 67]. In addition, [PERSON] and [PERSON] examined intricate mechanisms of auxeticity [30]. Last but not least, it has been observed that certain cooperative mechanisms exist in axial 3D models of many-body systems that exhibit square symmetry in the plane perpendicular to the axis. For instance, [PERSON] studied the purely geometric models of atomic auxetic systems [68] and auxetics with molecular inclusions [69]. In the present study, the utilization of static tensile tests and finite element numerical simulation analysis allowed for the quantification of variations in NPR and the elucidation of the deformation mechanism of lattice structures. The structure exhibited a significant NPR effect, and the magnitude of this effect was dependent on the geometric parameters. This study aims to extend the existing research model of NPR structures, thereby establishing a robust foundation for examining the performance of chiral and re-entrant NPR structures.