A modified Coulomb's law for the tangential debonding of osseointegrated implants

Cementless implants are widely used in orthopedic and dental surgery. However, debonding-related failure still occurs at the bone-implant interface. It remains difficult to predict such implant failure since the underlying osseointegration phenomena are still poorly understood. Especially in terms of friction and adhesion at the macroscale, there is a lack of data and reliable models. The aim of this work was to present a new friction formulation that can model the tangential contact behavior between osseointegrated implants and bone tissue, with focus on debonding. The classical Coulomb's law is combined with a state variable friction law to model a displacement-dependent friction coefficient. A smooth state function, based on the sliding distance, is used to model implant debonding. The formulation is implemented in a 3D nonlinear finite element framework, and it is calibrated with experimental data and compared to an analytical model for mode III cleavage of a coin-shaped, titanium implant (Mathieu et al. in J Mech Behav Biomed Mater 8(1):194-203, 2012). Overall, the results show a close agreement with the experimental data, especially the peak and the softening part of the torque curve with a relative error of less than 2.25%. In addition, better estimates of the bone's shear modulus and the adhesion energy are obtained. The proposed model is particularly suitable to account for partial osseointegration.