The medical application of implant replacements to remedy the pain in joints has necessitated a comprehensive study of wear due to contact of implant surfaces. Excessive wear can lead to toxicity and other implant associated medical issues such as patient discomfort and decreased mobility. Since implant wear is the result of contact between surfaces of tibia and talus implant, it is important to establish a model that can address implant surface contact mechanics with roughness effects. In this research, a statistical contact model is developed for the interaction of tibia and talus including normal and lateral contact in which surface roughness effects are included. The model accounts for the elastic–plastic interaction of the implant surface with roughness. For this purpose, tibia and talus implants are considered as macroscopic surfaces containing micron-scale roughness. Approximate equations are obtained that relate the contact force to the mean surface separation explicitly. Closed-form equations are obtained for hysteretic energy loss in implant using the approximate equations. Such a function can serve as a very useful tool for implant designers and manufacturers. Natural frequencies of both adduction-abduction and planter-dorsiflexion rotations are obtained using nonlinear vibration analyses.

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