Effective Young Modulus Evaluation of Bone–Titanium Biocomposite Formed Due to Complete Implant Osseointegration

The objective of study is to determine the effective Young modulus before and after the completed osseointegration process using mathematical modelling of a titanium porous structure. A novel model is proposed in the form of 3D arrays of Gibson-Ashby cells with rigid clamping of horizontal beams resting on elastic foundation. Calculations made on the basis of the developed model are compared with known models and literature data. The assumption is proved that the osseointegration process due to the bone tissues ingrowth into the pores of titanium implant could affect the Young modulus increasing its value in proportion to porosity of a specimen.