Effective compressive behavior of functionally graded TPMS titanium implants with ingrown cortical or trabecular bone

This work investigates numerically the effect of gradient coefficient, partial ingrowth length of bone, topology, loading direction, and average relative density on the yield strength (YS) and effective stiffness of functionally graded (FG) triply periodic minimal surface (TPMS)-based titanium implant topologically interconnected with ingrown bone subjected to uniaxial compression. The partially or fully topologic interconnection of two bi-continuous phases including titanium TPMS and bone forms a partially or fully interpenetrating phase composites (IPCs), for which their effective mechanical response is determined by means of finite element analysis and computational homogenization. The numerical framework used for this purpose is conceptually validated against the experimental characterization of the effective mechanical properties of additively manufactured two-phase FG IPC samples consisting of a white Polylactic Acid (PLA)-based reinforcement phase and white porous Polyvinyl Alcohol Natural (PVA)-based matrix phase under the same conditions such as the topology, dimensions, boundary conditions, and material property. The results show that the effective yield strength of the titanium-bone IPC increases with the decreased absolute value of the gradient coefficient regardless of the loading direction. Comparison between homogenization results obtained using titanium implant TPMS architectures with gyroid, primitive, diamond, and IWP shows that IWP exhibits the highest effective yield strength for a given porosity level. Moreover, the effective yield strength of the bone-implant FG IPCs increases with a rise of partial ingrowth length of bone and higher average relative density of the implant. The effective yield strength is also found to be substantially dependent on the direction of the applied load.