## 1 Introduction  
Cellular structures provide engineers and researchers with the possibilities of applying lightweight and high-energy absorption structures in sophisticated industries, such as the automotive, aerospace and shipbuilding industry. When the metal foams or honeycomb structures undergo compressive loading, the stress-strain curve usually experiences a long stress plateau before the densification. This is highly advantageous for applications as an energy absorber. The impact kinetic energy is effectively dissipated by transforming it into plastic strain energy with structural deformation. The successful utilization of cellular structures as protective shields in impact mitigation has drawn a lot of attention [1; 2; 3]. Apart from direct applications of cellular structures, they have been widely used as core structures of sandwich panels, which present a combination of high strength to weight ratio and excellent energy absorption capacity [4; 5]. Meanwhile, the concept of cellular structures filled with thin-wall composite structures has been proved to be effective in improving the energy absorption capacity [6; 7; 8]. Motivated by the potential enhancement in impact resistance, cellular structures possessing negative Poisson's ratio (NPR) have attracted considerable interest in the past few decades. The structures deform with the NPR effect, also known as auxetic structures or auxetics, shrink in the transverse direction when compressed in the longitudinal direction, and vice versa. Specifically, the shrinkage effect can densify the local material in the vicinity of the impact zone and further improve the impact resistance [9]. For isotropic and elastic materials, strain energy should satisfy the non-negativity requirement. Poisson's ratio can theoretically occur in a range between \(-1\) and \(1/2\)[10]. The existence of auxetic materials in the natural world was doubtful until [PERSON] [11] reported the NPR behavior of iron pyrite. To date, there are a number (more than 20 types) of natural materials and structures known to be auxetic and observed, for example, in the skin of mammals, certain forms of bone and crystalline solids [12; 13; 14; 15]. However, the naturally occurring auxetic materials are difficult to apply practically in protection engineering because of the lack of available candidate materials. Typically, technologies and measures, such as laser cutting, welding and water-jet cutting, are commonly applied in manufacturing two-dimensional (2D) auxetics [16; 17; 18], while manufacturing processes, such as artificial synthesis and three-dimensional (3D) printing, have usually been used for creating 3D auxetics [19; 20; 21]. In addition, 3D auxetics are also conceptualized from their 2D substructures. Regarding the in-plane impact performance of 2D auxetic structures, re-entrant honeycomb has been discussed the most. [PERSON] et al. [22] proposed a graded design of 2D re-entrant honeycomb by changing the cell wall angle along the crushing direction. Then, they numerically investigated the effectiveness of the angle-graded design in the enhancement of structural energy absorption capacity. They identified that the re-entrant honeycomb with angle-graded design absorbed more energy when subjected to quasi-static or low-speed impact loading. However, this enhanced energy absorption capacity could only happen to certain impact direction as increasing impact speed. In order to compare the impact performance between re-entrant honeycomb and hexagonal honeycomb, [PERSON] et al. [23] carried out a numerical study with the consideration of various values of crushing velocity. The results revealed that re-entrant honeycomb was superior in plastic energy absorption to conventional hexagonal honeycomb, which, however, exhibited lower peak stress at the same dissipated plastic energy. A similar conclusion was drawn by [PERSON] et al. [24] through an experimental and numerical investigation. [PERSON] et al. [25] and [PERSON] et al.