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

## TL;DR

This paper introduces a modified Coulomb's law with a state variable friction model to better predict tangential debonding of osseointegrated implants, improving accuracy over traditional models.

## Contribution

It presents a new friction formulation combining Coulomb's law with a displacement-dependent coefficient, calibrated with experimental data for enhanced debonding prediction.

## Key findings

- Close agreement with experimental torque data (error < 2.25%)
- Improved estimates of bone shear modulus and adhesion energy
- Effective modeling of partial osseointegration

## Abstract

Cementless implants are widely used in orthopedic and oral 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 macro-scale, there is a lack of data and reliable models. The aim of this work is 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. 2012). Overall, the results show 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, as is also shown.

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Source: https://tomesphere.com/paper/1908.04739