Design, simulation, and experimental validation of metamaterials with direction-dependent stiffness
Hossein Rahimi, Mahdi Khajepour, Davood Rahmatabadi, Ghader Faraji, Mostafa Baghani, Daniel George, Majid Baniassadi
Abstract
Mechanical metamaterials derive their functionality from geometry rather than composition, yet achieving experimentally validated three-dimensional direction-dependent stiffness (DDS) has remained challenging. This work introduces a 3D metamaterial unit cell with strong, tunable DDS, developed through a heuristic, gradient-free optimization framework that iteratively generated and refined geometries using finite element analysis. The final design features asymmetric internal struts and orientation-specific contact surfaces that activate bending- or stretching-dominated modes depending on loading direction. The unit cell and corresponding lattices were fabricated using high-resolution digital light processing (DLP) additive manufacturing and tested under compression along all three orthogonal axes. Simulations and experiments show excellent agreement (<1 % deviation), confirming distinct mechanical responses in the X, Y, and Z directions. The structure exhibits a stiffness increase above 350 % across deformation regions and up to 80 % contrast between its stiffest and most compliant orientations, while maintaining smooth force–displacement behavior with negligible stress concentrations. It also demonstrates substantial direction-dependent energy absorption, reaching several hundred joules in the stiffest orientation. These results establish a practical and manufacturable pathway toward architected materials with true 3D DDS, offering strong potential for exoskeletons, crash-protection systems, biomedical implants, and seismic-resistant components.