Analytical model of the elastic behavior of a modified face-centered cubic lattice structure.

As result of the advances made in additive manufacturing in recent years, the design of porous materials with controlled mechanical properties has gained importance due to their capability to offer case-specific solutions in multiple applications. In terms of biomaterials, the use of lattice structures provides a considerable variety of mechanical and geometric properties that can enhance osseointegration and reduce stress shielding. In this paper, the elastic response of a modified face-centered cubic (FCC) unit cell was studied, and analytical expressions for macroscopic effective Young's moduli, shear moduli and Poisson's ratios were obtained, thus providing the necessary parameters for the homogenization of the unit cell. The analytical expressions of the homogenization parameters open the possibility for implementation in other research fields, such as topology optimization. Timoshenko beam theory was used to model the struts of the modified FCC unit cell and a finite element analysis using shear flexible beam elements was performed to assess the accuracy of the analytical expressions. In addition to modelling the bending of the beams, axial and torsional displacements were also considered for a more detailed analysis. It can be concluded that the expressions obtained represent the elastic behavior of the modified FCC unit cell with high accuracy. Finally, the elastic response was further analyzed by introducing variability in the aspect ratio in order to enable the design of unit cells with controlled anisotropy.