A closed-form formulation for the conformal articulation of metal-on-polyethylene hip prostheses: contact mechanics and sliding distance

Using Hertz contact law results in inaccurate outcomes when applied to the soft conformal hip implants. The finite element method also involves huge computational time and power. In addition, the sliding distance computed using the Euler rotation method does not incorporate tribology of bearing surfaces, contact mechanics and inertia forces. This study, therefore, aimed to develop a nonlinear dynamic model based on the multibody dynamic methodology to predict contact pressure and sliding distance of metal-on-polyethylene hip prosthesis, simultaneously, under normal walking condition. A closed-form formulation of the contact stresses distributed over the articulating surfaces was derived based upon the elastic foundation model, which reduced computational time and cost significantly. Three-dimensional physiological loading and motions, inertia forces due to hip motion and energy loss during contact were incorporated to obtain contact properties and sliding distance. Comparing the outcomes with that available in the literature and a finite element analysis allowed for the validation of our approach. Contours of contact stresses and accumulated sliding distances at different instants of the walking gait cycle were investigated and discussed. It was shown that the contact point at each instant was located within the zone with the corresponding highest accumulated sliding distance. In addition, the maximum contact pressure and area took place at the stance phase with a single support. The stress distribution onto the cup surface also conformed to the contact point trajectory and the physiological loading.