Effect of mass multiple counting on the elastic properties of open-cell regular porous biomaterials

Low-density open-cell porous structures are widely researched due to their mechanical properties that are close to natural bone and their open-cell interconnected structure that allows for ingrowth of new bone tissue. Different studies have shown that apparent density dominates the mechanical properties of porous lattice structures. Surveying the literature revealed that in the previously published studies, there are inaccuracies in calculating the apparent density. In this study, the effects of considering exact apparent density rather than approximate density on the predicted elastic modulus, yield stress, and Poisson's ratio were investigated. The accuracy of the created models was evaluated by comparing their mechanical properties with corresponding experimental data. Five different types of unit cell, namely cube, rhombic dodecahedron, Weaire-Phelan, Kelvin, and diamond and three different cross-section geometries namely circle, square, and triangle were considered. The effects of unit cell type, cross-section type, and apparent density on the elastic moduli of open-cell tessellated cellular structures were also investigated. Considering exact density instead of approximate density increased the calculated elastic modulus and yield stress of structures with different morphologies by 22%-44% for an apparent density of 50%. Inversely, using exact apparent density instead of approximate apparent density decreased the Poisson's ratio values.