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Advances in additive manufacturing (AM) techniques have enabled fabrication of highly porous titanium implants that combine the excellent biocompatibility of bulk titanium with all the benefits that a regular volume-porous structure has to offer (e.g. lower stiffness values comparable to those of bone). Clinical application of such biomaterials requires thorough understanding of their mechanical behavior under loading. Computational models have been therefore developed by various groups for prediction of their quasi-static mechanical properties. The fatigue behavior of AM porous biomaterials is, however, not well understood. In particular, computational models predicting the fatigue response of these structures are rare. That is primarily due to the fact that geometrical features present in computational model of fully porous structures span over multiple length scales. This makes the problem formidably expensive to solve computationally. Here, we propose a multi-scale modeling approach to alleviate this problem and solve the problem of crack propagation in AM porous biomaterials. In this approach, the area around the crack tip is modelled at the micro-scale (using beam elements) while the area far from the crack tip is modeled at the macro-scale (using volumetric elements). Compact-tension notched specimens were fabricated using a selective laser melting machine for validating the results of the presented modeling approach. The multi-scale computational model was found to be capable of predicting the fatigue response observed in experiments., Accepted Author Manuscript, Biomaterials & Tissue Biomechanics

Additive manufacturing techniques have made it possible to create open-cell porous structures with arbitrary micro-geometrical characteristics. Since a wide range of micro-geometrical features is available for making an implant, having a comprehensive knowledge of the mechanical response of cellular structures is very useful. In this study, finite element simulations have been carried out to investigate the effect of structure unit cell type (cube, rhombic dodecahedron, Kelvin, Weaire-Phelan, and diamond), cross-section type (circular, square, and triangular), strut length, and relative density on the Young's modulus, shear modulus, yield stress, shear yield stress, and Poisson's ratio of open-cell tessellated cellular structures. It was desired to see whether or not and to what extent each of the aforementioned parameters affect the mechanical properties of a porous structure. It was seen that the strut cross-section type does not have a considerable effect on the structure Young's modulus while its effect on the structure yield stress is significant. The strut length was not effective on the mechanical properties if the relative density was kept constant. It was also observed that the structure unit cell type and relative density have a considerable effect on the elastic properties. The highest and the lowest stiffness and strength belonged to the cube and diamond unit cell types, respectively. The rhombic dodecahedron structure with circular cross-section had a high yielding strength (second among all the cases) while its Young's modulus was relatively low. Therefore, it is the best choice for applications with low stiffness requirements, such as biomedical implants., Accepted Author Manuscript, Biomaterials & Tissue Biomechanics