Modelling an orthopaedic knee prosthesis as a layered elastic system part 2: Finite element analysis

Abstract

This study deals with the development of a specialized finite element algorithm suitable for a non-linear contact stress analysis of a model of a plastic tibial plateau of a typical unicondylar knee prosthesis. The principle feature of the contact algorithm is the use of Lagrange multiplier methods for the application of displacement constraints to surface Gauss points of a contacting body to prevent mesh overlap. This allows the effective modelling of two- and three-dimensional contact problems, with or without friction, using higher order elements. Through the selection of suitable benchmark tests, the performance and accuracy of the algorithm was assessed prior to the model analysis. Good agreement was obtained between the finite element results for the contact model and existing theoretical and experimental data. It was found that the Hertzian theory failed to accurately predict localized stresses at the contact interface when the indenter was much stiffer than the model.