Abstract

Bovine Serum is the recommended lubricant for in-vitro wear testing of knee prostheses. However, bovine serum is a Newtonian fluid while synovial fluid has pseudolplastic characteristics, which means that the working conditions of the prostheses during the testing procedure could be different from the conditions existing in the knee. As a result, the lifetime predicted from in-vitro tests might be incorrect. In this work, a simplified visco-elastohydrodynamic lubrication model of a line contact representing a knee prosthesis under full flexion-extension motion is presented, considering a linear viscoelastic behavior for the tibial component and non-Newtonian behavior for the lubricant. The model is solved be means of the finite element method. The results show that the lubricating film thickness predicted when using a Newtonian model for the fluid is up to 70% higher than that found when the non-Newtonian model is implemented. Furthermore, the fluid film thickness is 45% narrower than the value computed for an elastic model when considering the viscoelastic behavior of the tibial component, which suggests that not only the rheology of the fluid is fundamental for a correct wear prediction, but also is the constitutive law of material deformation.

Abstract

Elastohydrodynamically lubricated contacts are an example of a strongly coupled fluid-structure interaction problem. Typically, these problems are solved in a partitioned way and require multiple flow-structure iterations per time step to reach convergence. The manner in which these iterations are performed is determined by the coupling algorithm. In the previous decade, several algorithms have been proposed, most of which are based on a quasi-Newton principle. These methods use an approximate Jacobian, which is constructed during the calculation itself. However, in many cases, a simpler model is available, which provides an approximate solution and Jacobian, and is denoted as surrogate model. For the elastohydrodynamically lubricated contact, this model is the coupled Reynolds-Boussinesq approach, which evaluates significantly faster than the CFD-CSM simulation. The incorporation of a surrogate model in a quasi-Newton method is realized with the IQN-ILSM algorithm. This work is a first step towards employing this coupling method for the elastohydrodynamically lubricated contact and, in this way, combining the speed of the Reynolds-Boussinesq approach with the accuracy and versatility of the CFD-CSM modelling. In the current work, only the surrogate solution will be used as initial solution. The use of the surrogate Jacobian is future work.