Viscoelastic Behavior of Cellular Biomaterials Based on Octet-Truss and Tetrahedron Topologies

Cellular biomaterials offer unique properties for diverse biomedical applications. However, their complex viscoelastic behavior requires careful consideration for design optimization. This study explores the effective viscoelastic response of two promising unit cell designs (tetrahedron-based and octet-truss) suitable for high porosity and strong mechanics. The asymptotic homogenization (AH) method was employed to determine effective longitudinal and shear moduli, as well as Poisson’s ratio, across various relative densities. Finite element simulations (ABAQUS) validated the AH results, demonstrating good agreement (<10% discrepancies). Additionally, analytical models and compression tests on 3D-printed lattice structures supported the theoretical predictions. The study revealed a strong correlation between relative density and the effective modulus of both designs. Notably, the tetrahedron-based design exhibited superior modulus, making it favorable for high loading levels, particularly when used as a high-density configuration. Both designs demonstrated minimal time-dependent elastic modulus changes and a near-constant Poisson’s ratio (0.34–0.349 for octet-truss, 0.316–0.326 for tetrahedron) across a 5–50% relative density range. While minimal, time-dependent modulus reduction needs to be considered in longer-term simulations ($t>{10}^7$ $\mathrm{s}$). This study provides valuable insights into the viscoelastic behavior of these unit cells using the homogenization method, with potential applications in various biomedical fields.