A simple fully integrated contact-coupled wear prediction for ultra-high molecular weight polyethylene hip implants

A fully coupled contact and wear model was developed in the present study for hip implants employing an ultra-high molecular weight polyethylene (UHMWPE) cup in combination with a metallic or ceramic femoral head. A simple elasticity equation based on the concept of constrained column model was employed to solve the contact mechanics between the acetabular cup and the femoral head under the three-dimensional physiological loading condition. The wear model was based on the classical Archard - Lancaster equation in common with all other studies reported in the literature. The fully coupled contact and wear model was applied to both conventional and cross-linked UHMWPE cups under a wide range of design parameters such as the clearance and the femoral head radius. The predicted linear and volumetric wear as well as their rates for conventional UHMWPE cups were found to be in good agreement with those obtained from a similar analysis by Maxian but using the finite element method for the contact mechanics analysis. The predicted maximum contact pressure was found to decrease rapidly within the first 106 cycles, and below the limit to cause plastic deformation within the UHMWPE cup with a nominal radial clearance of 0.2 mm. The effect of the clearance between the head and the cup on the predicted wear was found to be negligible. For the cross-linked UHMWPE cup with relatively large diameters up to 48 mm and a fixed outside diameter of 50 mm, the predicted wear, which was found to increase with increasing femoral head radius, remained small owing to the small wear factor associated with these materials. Furthermore, if the head diameter increases beyond 42 mm, a rapid increase in the contact pressure was predicted, owing to the decrease in the wall thickness of the cross-linked UHMWPE cup.