This research is aimed at proposing an enhanced re-entrant hexagonal structure and examining its auxetic behavior in compressive or tensile load conditions. An integrated experimental and finite element analysis (FEA) approach was used to investigate the behavior of the proposed structures in combination with polymeric materials (thermoplastic polyurethane (TPU) materials such as Ninjaflex® and Semiflex®). We focused on the effect of nonlinearity of the structure on the overall stiffness and shock-absorption performance of the body protection pads. FEA models were used to examine how the stiffness and Poisson’s ratio are affected by static load conditions and also how the dynamic loads are transmitted through the auxetic structure. The static FEA models were verified through experimental testing. Advanced additive manufacturing (3D printing) techniques such as Fused Deposition Modeling (FDM) were used to build fixtures and prototypes of the auxetic polymeric structures. Structural stiffness and Poisson’s ratio were examined not only in tensile loading condition but also in compression. Axial and lateral deformations were measured for given axial forces on the experimental model, and the measured values of Poisson’s ratio were compared with the computational results. It was shown that the enhanced re-entrant hexagonal structures had nonlinear behavior, which could be a useful property for developing body protection pads and stiffness-varying structures.