## 1 Introduction
[PERSON] [28] manufactured different unit cell combinations of octahedral and pillar micro-lattice structures using PBF to be used for load bearing applications. The cross-section of the fabricated struts exhibited elliptical shape as opposed to the designed circular shape, impacting the mechanical behaviour of the samples. [PERSON] [27] provided a comprehensive summary of cellular structures and in-depth analysis and validation of PBF capabilities, providing insight into the effect of processing parameters on strut quality and concluding that good quality struts are produced by minimum exposure time and minimum exposure area, and indicating a strong relationship between strut diameter and amount of energy deposited. [PERSON] [29] manufactured four different cell types of triply periodic minimal surface (TPMS) cellular structures from three metallic powders 316L, Ti-6 Al-4V and AlSi10 Mg) using PBF. Computer tomography (CT) analysis carried out on the samples showed no major geometry defects, which confirmed the ability of PBF to manufacture a wide range of cellular structures. An increase in the thickness of the struts was observed due to the increased energy concentration on the small struts. [PERSON] [30] performed detailed analysis of mechanical, dimensional and geometrical properties of Ti-6 Al-4V body-centred cubic (BCC) micro-lattice structures manufactured by PBF, and demonstrated the benefit of a heat treatment in improving the mechanical properties and dimensional accuracy of the samples. [PERSON] et al. [31] investigated scanning strategies for PBF of micro-lattices and concluded that random paths with track overlapping as a strategy to improve density and mechanical properties. [PERSON] studied the possibility of manufacturing 3D re-entrant structures using PBF from shape memory alloys (SMA) [32], however, [PERSON] was forced to modify the auxetic design to overcome the limitation of PBF in manufacturing overhanging structures, which compromised [PERSON]'s ratio. [PERSON] [33] and [PERSON] [34] manufactured metal 3D auxetic structures with re-entrant configuration using the selective electron beam melting (SEBM) process, but the fabricated structures had issues with quality in the form of surface roughness and dimensional accuracy, which prevented the structures being used for bio-medical applications, especially in implants such as hip stems and spinal vertebral discs [35]. There is, therefore, a need for a manufacturing process that can provide good control over surface roughness, dimensional accuracy and mechanical properties of the auxetic structures. There has been no systematic study of the capability of PBF in manufacturing a wide range of re-entrant unit cell configurations and the influence of unit cell design parameters on their mechanical properties. There are also contradictions between the experimental mechanical test results of PBF re-entrant structures and theoretical models due to the induced torsional moments, internal stresses in the struts, and manufacturing defects [34]; thus, there is need to verify the assumptions made for the deforming mechanism in [PERSON]'s theoretical model using experimental methods such as digital image correlation (DIC). This research therefore aims to address these gaps by studying the feasibility of using laser-PBF for a wide range of re-entrant unit cell configurations and developing a methodology which forms a basis for using PBF for manufacturing metallic 3D auxetic structures.