Abstract
Introduction
The input mechanical properties of knee replacement bearing materials, such as elastic modulus and Poisson's ratio, significantly contribute to the accuracy of computational models. They should therefore be determined from independent experimental studies, under similar test conditions to the clinical and experimental conditions, to provide reliability to the models. In most cases, the reported values in the literature for the elastic modulus and Poisson's ratio of the bearing materials have been measured under tensile test conditions, in contrast to the compressive operating conditions of the total knee replacements (TKR). This study experimentally determined the elastic modulus and Poisson's ratio of conventional and moderately cross-linked ultra-high molecular weight polyethylene (UHMWPE) under compressive test conditions. These material parameters will be inputs to future computational models of TKR.
Materials/Methods
To determine the Poisson's ratio of the conventional and moderately cross-linked UHMWPE, contact areas of 12mm diameter cylindrical specimens of 10.2mm length were measured experimentally under a compressive displacement of 1mm, at a strain rate of 12mm/min that was held for 10minutes. A computational model was developed in Abaqus, 6.14–1, to simulate this experimental test assuming different values for the Poisson's ratio of the UHMWPE cylindrical specimens. The curve fitted relationship between the computationally predicted contact area and Poisson's ratio was used to calculate the Poisson's ratio of the UHMWPE specimens, using the experimentally measured contact areas. Using a similar approach, the equivalent elastic modulus of the UHMWPE was calculated using the computationally calculated curve fitted contact area-elastic modulus relationship, from the computational simulation of a ball-on-flat compression test, and the experimentally measured contact area from a ball-on-flat dynamic compression test. This experiment used 10mm thick UHMWPE flat specimens against a 63.5mm rigid ball, under a compressive dynamic sinusoidal loading of 250N average load, and 6000 cycles. The applied test conditions maintained the stress level within the reported range for the TKR.
Results
The predicted maximum contact stress was 26 and 35 [MPa] for the conventional and moderately cross-linked UHMWPE respectively. The measured Poisson's ratio was 0.33±0.04 (mean ± 95% confidence interval (CI), n=5) and 0.32±0.08 (mean ± 95% CI, n=3) for conventional and moderately cross-linked UHMWPE respectively. The corresponding values for the equivalent elastic modulus were 365±31 and 553±51 [MPa] (mean ± 95% CI, n=3) respectively (Fig.1).
Discussion
The Poisson's ratios and elastic moduli for the conventional and moderately cross-linked UHMWPE materials were more than 20% lower than values reported in literature that have been measured under tensile test conditions [1–3]. Computational wear models adopting mechanical properties of the bearing materials delivered under more realistic compressive loading conditions are more appropriate.
Conclusion
The current study presented a reverse engineering approach to characterise the mechanical properties of conventional and moderately cross-linked UHMWPE for TKR bearing materials, under realistic compressive test conditions. The measured mechanical properties, were lower than that reported in literature under tensile loading conditions, and should be adopted in future computational models of TKR for a more realistic and robust virtual modelling platform.
