TPMS sheet structures with orthorhombic symmetry: Anisotropic elasticity and energy absorption

• Orthorhombic TPMS lattices studied for anisotropic mechanical performance. • Experiments and FEA reveal topology- and orientation-dependent behavior. • Novel method links surface geometry to stiffness via orientation tensors. • Scaling laws predict stiffness, strength, and energy absorption from geometry. • Results support geometry-driven design of anisotropic architected materials. Triply periodic minimal surface (TPMS) architectures have gained prominence as high-performance cellular structures due to their smooth geometry, load-bearing efficiency, and suitability for additive manufacturing. While prior work has explored TPMS lattices with cubic symmetry, this is the first study to systematically evaluate orthorhombic TPMS lattices using a combined experimental, finite element analysis (FEA), and orientation tensor approach to derive predictive structure–property scaling laws. This study investigates the anisotropic elastic and energy absorption characteristics of four orthorhombic TPMS topologies (CLP, I-6, I-8, and I-9) through a combination of FEA, geometric orientation tensor analysis, and experimental compression testing. Thin-walled TPMS specimens (0.3 mm thickness) were additively manufactured and tested along three orthogonal directions. A novel, interpretable method is proposed to relate directional stiffness and energy absorption to the eigenvalues of orientation tensors derived from surface geometry. The results reveal topology-dependent scaling laws that capture the influence of anisotropy and relative density on mechanical response. Experimental and simulated outcomes show strong agreement, validating the predictive capability of the geometric scaling models. These findings provide new insights into the structure-property relationships of anisotropic shell-based cellular solids, enabling more efficient and targeted design of multifunctional architected cellular materials.