<p>Auxetic structures have gained extensive demand in the field of biomedical, aerospace and textile applications owing to the unique characteristics of negative Poisson’s ratio with enhanced energy absorption properties. The present work investigates the effects of geometrical parameters of the re-entrant type auxetic structure on the apparent density, energy absorption and Poisson’s ratio. The major geometrical parameters such as re-entrant angle, strut thickness and radius of curvature of the unit cell of auxetic structure were selected for the investigation. The geometrical parameters were suitably varied, and experimental runs were planned as per the Central Composite Design (CCD) to investigate the effects of geometrical parameters on the physical and mechanical properties of the auxetic structures. The auxetic structures as per the design of experiments (DOE) were additively manufactured using standard Fused Deposition Modelling (FDM). The apparent density was measured using Archimedes’ density measurement method, energy absorption and Poisson’s ratio were measured using deformation behavior during uniaxial compression test. From the experimental investigations, it was found that the apparent density increased with the increase in the strut thickness and re-entrant angle whereas it was reduced with the increase in radius of curvature of the structure. Strut thickness contributed the most affecting the energy absorption followed by re-entrant angle and radius of curvature. Further, increase in strut thickness increased Poisson’s ratio reducing the auxetic nature of the printed structure unlike re-entrant angle and radius of curvature. Additionally, multi-objective optimization was performed using Genetic Algorithm to find out the magnitudes of optimal geometric parameters for minimizing apparent density, Poisson’s ratio and maximizing energy absorption. Finally, case studies were performed by comparing the mechanical characteristics of the present optimal conditions with the results of existing reports.</p> Graphical abstract <p> The present work highlights the investigations on the performances of auxetic structures with varying geometric parameters such as thickness, re-entrant angle, and radius of curvature. Central composite design (CCD) was used to generate geometric parameter combinations, which were modelled and fabricated using Fused Deposition Modelling (FDM). Output responses such as apparent density, energy absorption, and Poisson’s Ratio were measured using the liquid displacement method, compressions tests and image analysis of deformed structure respectively. The effects of geometrical parameters and their interactions were investigated using statistical tools and optimal conditions were found out using Genetic Algorithm. Finally, confirmatory tests and a case study were conducted to compare optimized designs with existing reports.</p>