# Impact Testing of 3D Re-Entrant Honeycomb Polyamide Structure Using Split Hopkinson Pressure Bar
## 1 Introduction  
Both auxetic materials and structures exhibit the characteristic of a negative Poisson's ratio, expanding in the lateral direction when stretched and contracting when compressed, which is contrary to the positive Poisson's ratio properties of general materials and structures and is also known as auxetic behaviour. The negative Poisson's ratio is a scale-independent property in the theory of elasticity, which means the auxetic behaviour can be obtained at different scale levels [1, 2]. Due to the auxetic characteristic, it has some excellent properties, such as increased shear modulus [3, 4], increased indentation resistance [3, 5], high fracture toughness [6, 7], high energy absorption [8, 9] and unique acoustic absorption [10]. Therefore, it is widely used in aerospace, protection, biomedicine, manufacturing, sports, sensors and other fields [1]. Over the last three decades, many studies have been conducted on the theoretical, experimental and numerical simulation of negative Poisson's ratio materials and structures. [PERSON] et al. [11] dealt with the calculation of the basic mechanical properties of RH structures by using the energy methods of solid mechanics along with numerical methods. [PERSON] et al. [12] theoretically analysed the three-dimensional (3D) RH auxetic structures based on both a small deflection model and large deflection model. [PERSON] et al. [13, 14] establishedan analytical model of a 3D RH auxetic cellular structure based on the energy method to study the mechanical properties and introduced the interlocking assembly method into the fabrication of 3D periodic auxetic cellular structure. In the work of [PERSON] et al. [15; 16], 3D-printed trapezoidal sandwich structures were designed to determine the quasi-static indentation response and failure mode, and 3D-printed corrugated sandwich structures were designed to monitor the crack initiation and crack propagation using the acoustic emission technique. [PERSON] et al. [17] present a comparative study of two-dimensional (2D) and 3D auxetic geometries by using CAD-CAE tools. However, there are still many problems to be further explored. In terms of application, although there are many potential applications, most of them remain in the theoretical and experimental stage. The immature research on the basic characteristics of 3D materials and structures such as dynamic mechanical behaviours, and the high manufacturing cost limit their practical application. The 3D re-entrant honeycomb (RH) structure is a typical auxetic structure, as shown in Figure 1b. The deep study on its static and dynamic mechanical behaviours will help us to further explore other auxetic materials and structures. Although many related studies have been carried out on the RH structure, most of them are based on the 2D structure [18; 19; 20; 21], and studies on the dynamic properties of the 3D RH structure are rare. The limited research on 3D RH dynamic experiments is mainly focused on sandwich plates with an auxetic core [22; 23], while the research on the 3D RH structure itself is very limited [24]. On the other hand, with the rise of the additive manufacturing (AM) technique in recent years, it is possible to manufacture complex 3D structures. Among the materials used in AM, polymers [25; 26] are by far the most utilized class of materials for AM [26]. Polyamide, as one of the dominant market shares of polymers, has high strength, high stiffness and excellent long-term performance [27]. It is worth noting that there is no previous study on the dynamic properties of a 3D RH structure made of polyamide in the literature. Therefore, it is necessary to study the dynamic properties of the newly developed 3D re-entrant structure made of polyamide under impact loading. In this study, 3D RH auxetic structures made of polyamide were further studied for their dynamic impact properties on the basis of the previous study on their quasi-static mechanical properties [28]. Firstly, 3D RH polyamide structure specimens were printed by AM technology.