Evaluation of the Orthotropic Behavior in an Auxetic Structure Based on a Novel Design Parameter of a Square Cell with Re-Entrant Struts

In this research, a three-dimensional auxetic configuration based on a known re-entrant cell is proposed. The 3D auxetic cell is configured from a new design parameter that produces an internal rotation angle to its re-entrant elements to study elastic properties in its three orthogonal directions. Through a topological analysis using Timoshenko beam theory, the bending of its re-entrant struts is modeled as a function of the new design parameter to manipulate Poisson's ratio and Young's modulus. Experimental samples were fabricated using a fused filament fabrication system using ABS and subsequently tested under quasi-static compression and bending tests. Additionally, an orthotropy factor is applied that allows for measuring the deviation between the mechanical properties of each structure. The experimental results validate the theoretical design and show that this new unit cell can transmit an orthotropic mechanical behavior to the macrostructure. In addition, the proposed structure can provide a different bending stiffness behavior in up to three working directions, which allows the application under different conditions of external forces, such as a prosthetic ankle.