## 1 Introduction  
Material with negative Poisson's ratio was initially observed by [PERSON] in 1892 in the form of single crystal pyrite with Poisson's ratio -0.14 [1]. The term \"auxetic\" was coined in 1991 by [PERSON] [2] for materials with negative Poisson's ratio, which is derived from the Greek word \"auxetickos\" which means \"that which tends to increase\" [2]. Re-entrant geometry is formed by inverting the diagonal struts in the normal hexagonal honeycomb geometry. Re-entrant geometry was initially presented by [PERSON] [3], and then by [PERSON] [4] who developed auxetic structures made of rods, hinges and springs based on re-entrant geometry. [PERSON] developed computer models of hard [5] and soft [6] cyclic hexamers and demonstrated that they exhibited phases having negative Poisson's ratio, and more recently, a strongly anisotropic chiral phase of negative Poisson's ratio was found in a work about hard cyclic tetramers [7]. Re-entrant structure was also observed in auxetic foams formed by the volumetric compression of conventional foams, with ribs that permanently protrude inwards forming a re-entrant structure [8]. Re-entrant honeycombs also deform by flexure, stretching of the struts, as well as the hinging mechanism of the strut joints [9]. A wide range of other auxetic structure models has been developed, including the triangular variation of re-entrant structure, proposed by [PERSON] et al [10]; the chiral honeycomb model, first introduced by [PERSON] [11], and further described by [PERSON] and [PERSON] [12], made up of circular nodes connected by the straight ligaments in a tangential manner; the rotating rigid unit model, which was first introduced by [PERSON] and [PERSON] [13] and, independently, by [PERSON] and [PERSON] [14] in the same year, in the form of rigid squares connected at the vertices by hinges; the missing rib model, proposed by [PERSON] [15] as an alternative to the re-entrant model due to presence of the broken ribs in transformed auxetic foams; and the nodule fibril model, proposed by [PERSON] and [PERSON] [9], consisting of a network of nodules interconnected by fibrils. Auxetic structures are known for their enhanced mechanical, electromagnetic and acoustic properties. Mechanical properties include increased indentation resistance, energy dissipation capacity, bending stiffness, toughness, shear resistance and fatigue resistance [16]. Apart from mechanical properties, auxetic structures also possess increased di-electric and sound absorption capability compared to conventional materials [17; 18]. Due to their enhanced properties, auxetic structures find application in various fields, namely, automotive, aerospace, military, biomedical etc. Some of the applications include sandwich structures, energy absorbing materials, bio-medical implants, knee cap, blast proof curtains, safety jackets, helmets etc. [16; 19; 20]. There has been a recent rapid growth in interest in auxetic structures, particularly in their application in civil engineering, e.g., as damping elements for seismic protection [21], and as damage tolerant building materials [22], as well as new smart metamaterials [23; 24]. Though various 2D auxetic models have been previously manufactured successfully, it has been a challenge to manufacture 3D auxetic structures, especially in metal. Due to their structural complexity, they cannot be manufactured using conventional manufacturing processes. Initially, [PERSON] and [PERSON] [25] transformed conventional metallic foams into auxetic foams with 3D re-entrant structures using a thermal compression and expansion process, although this provided limited control over the dimensional and mechanical properties of the structure. Powder bed fusion (PBF) additive manufacturing (AM), a layer AM process, building parts via the selective laser fusion of metal powder layers, offers the ability to manufacture complex metal parts, with lattice structure [26; 27] and, therefore, could enable manufacture of complex 3D auxetic structures.