An axisymmetric contact model of ultra high molecular weight polyethylene cups against metallic femoral heads for artificial hip joint replacements.

Contact mechanics of ultra high molecular weight polyethylene (UHMWPE) cups against metallic femoral heads for artificial hip joints is considered in this study. Both the experimental measurement of the contact area and the finite element prediction of the contact radius, maximum contact pressure and maximum Von Mises stress have been carried out for a wide range of contemporary artificial hip joints. Good agreement of the contact radius has been found between the experimental measurements and the finite element predictions based upon an elastic modulus of 1000 MPa and a Poisson's ratio of 0.4 for UHMWPE material under various loads up to 2.5 kN. It has been shown that the half contact angle for all the cup/head combinations considered in this study is between 40 degrees and 50 degrees under a load of 2.5 kN. The importance of this result has been discussed with respect to the anatomical position of the cup when placed in the body and the selection of a simple wear-screening test for artificial hip joints. The predicted contact radius and maximum contact pressure from the finite element model have also been compared with a simple elasticity analysis. It has been shown that the difference in the predicted contact radius between the two methods is reduced for more conforming contacts between the femoral head and the acetabular cup and smaller UHMWPE cup thickness. However, good agreement of the predicted maximum contact pressure has been found for all the combinations of the femoral head and the acetabular cup considered in this study. The importance of contact mechanics on the clinical performance of artificial hip joint replacements has also been discussed.     

A general axisymmetric contact mechanics model for layered surfaces, with particular reference to artificial hip joint replacements

A general axisymmetric contact mechanics model for layered surfaces is considered in this study, with particular reference to artificial hip joint replacements. The indenting surface, which represents the femoral head, was modelled as an elastic solid with or without coating, while the other contacting surface, which represents the acetabular cup, was modelled as a two-layered solid. It is shown that this model is applicable to current total hip joint prostheses employing ultra-high molecular weight polyethylene (UHMWPE) acetabular cups against metallic, metallic with coating or ceramic femoral heads as well as metal-on-metal combinations. The effect of cement is also investigated for these prostheses using this model. The use of a metallic bearing surface bonded to a UHMWPE substrate for acetabular cups is particularly examined for metal-on-metal hip joint replacements. Both the contact radius and the contact pressure distribution are predicted for examples of these total hip joint replacements, under typical conditions. Application of contact mechanics to the design of artificial hip joint replacements employing various material combinations is discussed.     

Steady-state elastohydrodynamic lubrication analysis of a metal-on-metal hip implant employing a metallic cup with an ultra-high molecular weight polyethylene backing

The elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a 28 mm diameter metal-on-metal hip prosthesis employing a metallic cup with an ultra-high molecular weight polyethylene (UHMWPE) backing under a simple steady state rotation representing the flexion/extension during walking. Both Reynolds and elasticity equations were coupled and solved numerically by the finite difference method. The elastic deformation was determined by means of the fast Fourier transform (FFT) technique using the displacement coefficients obtained from the finite element method. Excellent agreement of the predicted elastic deformation was obtained between the FFT technique and the conventional direct summation method. The number of grid points used in the lubrication analysis was found to be important in predicting accurate film thicknesses, particularly at low viscosities representative of physiological lubricants. The effect of the clearance between the femoral head and the acetabular cup on the predicted lubricant film thickness was shown to be significant, while the effect of load was found to be negligible. Overall, the UHMWPE backing was found not only to reduce the contact pressure as identified in a previous study by the authors (Liu et al., 2003) but also significantly to increase the lubricant film thickness for the 28 mm diameter metal-on-metal hip implant, as compared with a metallic mono-block cup.     

A new formulation for the prediction of polyethylene wear in artificial hip joints

Artificial joints employing ultra-high molecular weight polyethylene (UHMWPE) are widely used to treat joint diseases and trauma. Wear of the polymer bearing surface largely limits the use of these joints in younger and more active patients. Previous studies have shown the wear factor used in Archard's law for the conventional polyethylene to be highly dependent on contact pressure and this has produced variability in experimental data and has constrained the reliability and applicability of previous computational predictions. A new wear law is proposed, based on wear volume being dependent on, and proportional to, the product of the sliding distance and contact area. The dimensionless proportional constant, wear coefficient, which was independent of contact pressure, was determined from a multi-directional pin on plate study. This was used in computational predictions of the wear of the conventional UHMWPE hip joints. The wear of the polyethylene cup was independently experimentally determined in physiological full hip joint simulator studies. The predicted wear rate from the new computational model was generally increased, with an improved agreement with the experimental measurement compared with the previous computational model. It was shown that wear in the UHMWPE hip joints increased as head size and contact area increased. This resulted in a much larger increase in the wear rate as the head size increased, compared with the previous computational model, and is consistent with clinical observations. This new understanding of the wear mechanism in artificial joints using the UHMWPE bearing surfaces, and the improved ability to predict wear independently and to address previously described discrepancies offer new opportunities to optimize design parameters.     

Prediction of scratch resistance of cobalt chromium alloy bearing surface, articulating against ultra-high molecular weight polyethylene, due to third-body wear particles

The entrapment of abrasive particles within the articulation between a cobalt chromium alloy (CoCrMo) femoral component and an ultra-high molecular weight polyethylene (UHMWPE) cup of artificial hip joints or tibial inserts of artificial knee joints usually scratches the metallic bearing surface and consequently increases the surface roughness. This has been recognized as one of the main causes of excessive polyethylene wear, leading to osteolysis and loosening of the prosthetic components. The purpose of this study was to use the finite element method to investigate the resistance of the cobalt chromium alloy bearing surface to plastic deformation, as a first approximation to causing scratches, due to various entrapped debris such as bone, CoCrMo and ZrO2 (contained in radiopaque polymethyl methacrylate cement). A simple axisymmetric micro contact mechanics model was developed, where a spherical third-body wear particle was indented between the two bearing surfaces, modelled as two solid cylinders of a given diameter, under the contact pressure determined from macro-models representing either hip or knee implants. The deformation of both the wear particle and the bearing surfaces was modelled and was treated as elastic-plastic. The indented peak-to-valley height on the CoCrMo bearing surface from the finite element model was found to be in good agreement with that reported in a previous study when the third-body wear particle was assumed to be rigid. Under the physiological contact pressure experienced in both hip and knee implants, ZrO2 wear particles were found to be fully embedded within the UHMWPE bearing surface, and the maximum von Mises stresses within the CoCrMo bearing surface reached the corresponding yield strength. Consequently, the CoCrMo bearing surface was deformed plastically and the corresponding peak-to-valley height (surface roughness) was found to increase with both the hardness and the size of the wear particle. Even in the case of CoCrMo wear particles, with similar mechanical properties to those of the CoCrMo bearing surface, a significant plastic deformation of the bearing surface was also noted; this highlighted the importance of considering the deformation of the wear particles. These findings support the hypotheses made by clinical studies on the contribution of entrapped debris to increased surface roughness of CoCrMo femoral bearing surfaces.     

A simulator study of friction in total replacement hip joints.

Frictional behaviour of 22 different femoral head-acetabular cup combinations was studied on a new servo-hydraulic microcomputer-controlled hip joint simulator using various flexion-extension angle and superior-inferior load set value waveforms and using distilled water at 37 +/- 1 degrees C as lubricant. Six different head materials were included in the study, whereas all cups were ultra-high molecular weight polyethylene (UHMWPE). Most head-cup combinations studied are commercially available. No distinctly superior joint design can be pointed out, but the frictional behaviour of alumina ceramic against UHMWPE proved overall most favourable (mu min was 0.02), whereas that of non-ion-implanted titanium alloy Ti-6Al-4V against UHMWPE proved strikingly poor (mu max was 0.15). The lowest frictional torque was in 22 mm joints, but frictional torque did not always increase straightforwardly with increasing diameter of the femoral head. The measurements form an extensive comparison between a wide variety of head-cup combinations. The simulator is apparently a useful instrument in the study of frictional behaviour of new designs, materials, surface treatments and coatings that are frequently introduced.     

Temperature prediction in a finite element model for sliding contact analysis of total hip prosthesis

A finite-element model for sliding contact in total hip joint prosthesis is presented in this paper. The hip prosthesis studied consists of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup articulating against cobalt-chrome and alumina-ceramic femoral heads. Various aspects of prosthesis operation were analysed using the finite-element model. For example, bulk material and surface stresses were analysed under varying conditions of elastic modulus, friction coefficient, sliding speed, and radial clearance. The resulting variations of temperature were also recorded. The results obtained from the model are useful in understanding the operating conditions and the causes of wear in the hip prosthesis.     

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 10(6) 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.     

Improved mathematical model of the wear of the cup articular surface in hip joint prostheses and comparison with retrieved components

This paper presents an analytical model of the cobalt-based alloy-ultra-high molecular weight polyethylene (UHMWPE) wear coupling. Based on a previous model in which the cup wear volume over a gait cycle (WG) was calculated under the simplifying assumption of an ideal rigid coupling, the current version proposes a more realistic wear simulation. All three components of the hip loading force were considered for the contact pressure calculation and all three components of the hip motion were taken into account for the sliding distance calculation. The contact pressure distribution was calculated on the basis of the Hertzian theory for the elastic contact of two bodies with non-conforming geometrical shapes. The wear factor was taken from hip simulator wear tests. The calculated WG is 67 x 10(-6) mm3 for a standard reference patient. The parametric model simulations show that WG increases linearly with the patient weight, femoral head diameter and surface roughness. It increases non-linearly to a maximum and decreases to an asymptotic value with increasing cup/head clearance and with cup isotropic elastic modulus. The cup orientation in the pelvis affects only slightly the total amount of WG whereas it is the dominant factor affecting the shape of the wear distribution. The iso-wear maps show paracentral patterns at low cup inclination angles and marginal patterns at higher inclination angles. The maximum wear depth is supero-posterior when the cup is in neutral alignment and supero-anterior at increasing anteversion angles. Complex patterns with a combination of paracentral and marginal wear were obtained at specific clearance values and cup orientations. The results of the simulations are discussed in relation to the wear distribution measured on the articular surface of 12 UHMWPE components retrieved from failed hip joint prostheses, after a period of in situ functioning.     

Elastohydrodynamic lubrication analysis of metal-on-metal hip prostheses under steady state entraining motion

The elastohydrodynamic lubrication problem of metal-on-metal hip joint replacements was considered in this study. A simple ball-in-socket configuration was used to represent the hip prosthesis. The Reynolds equation in a spherical coordinate was adopted for the fluid-film lubrication analysis, to account for the ball-in-socket geometry. The corresponding elastic deformation was calculated by means of the finite element method in order to consider the complex ball-in-socket geometry as well as the backing materials underneath the acetabular cup. Both the Reynolds and the elasticity equations were solved simultaneously using the Newton-Raphson finite difference method. The general methodology developed was then applied to a recent experimental prototype metal-on-metal hip implant. It was shown that the backing materials underneath the acetabular cup had little influence on the predicted contact pressure and the elastic deformation at the bearing surfaces for this particular example. Both the film thickness and the hydrodynamic pressure distributions were obtained under various loads up to 2500 N. The predicted minimum lubricating film thickness from the present study was compared with a simple estimation using the Hamrock and Dowson formulae based upon an equivalent ball-on-plane model and excellent agreement was found. However, it was pointed out that for some forms of metal-on-metal hip prostheses with a thin acetabular cup, a polyethylene inlay underneath a metallic bearing insert or a taper connection between a bearing insert and a fixation shell, the general methodology developed in the present study should be used and this will be considered in future studies.     

Effect of elastic-plastic behavior of coating layer on drawability and frictional characteristic of galvannealed steel sheets

During a galvannealed sheet metal forming, the failures of coating layers (powdering, flaking and cracking) frequently affect the strain state of sheets and deteriorate the frictional characteristic between sheets and tools. Two FE-models in this study were suggested to investigate the effects of the mechanical behavior of coating layers on the formability and friction of the coated steel sheets in FE analysis; the first is one-layer model to express the coated sheet as one stress-strain curve and the second is a multiple-layer model which is composed of substrates and coating layers, separately. First, the frictional properties and the formability of the coated sheets were experimentally investigated using a cup deep-drawing trial. After, the drawing process was simulated by FE analysis of the two models. In the multiplelayer model, the mechanical behavior of the coating is defined as a stress-strain curve which was determined using the nanoindentation test of the coating, its FE analysis and artificial neural network method. The result showed that the multiple-layer model provides more accuracy predictions of drawing loads than the one-layer model in the FE analysis, compared to the actual cup drawing test.

     

A Method of Calculation for Contact Pressure between Femoral Head and Cup of Artificial Hip Joint

Abstract

A method of calculation for contact pressure between a hard femoral head and soft plastic cup of a hip joint was studied. Providing that the contact pressure is proportional to the radial deformation of the cup, an equation of equilibrium in terms of a nondimensional parameter was derived. Once the magnitude of the parameter is determined by solving the equation, the contact pressure distribution is easily obtained. An effect of the radial clearance between a femoral head and cup on contact pressure was evaluated using the equation. Furthermore, the effect of Young's modulus and thickness of a plastic cup on contact pressure were also evaluated. According to the results, contact pressure increased with an increment of clearance and Young's modulus. The contact pressure increased with a decrement of thickness of the plastic cup. The analytical solution was compared with the finite element method (FEM) analysis and the agreement was confirmed. An equation of frictional torque was also derived     

Elastohydrodynamic lubrication analysis of ultra-high molecular weight polyethylene hip joint replacements under squeeze-film motion

Elastohydrodynamic lubrication was analysed under squeeze-film or normal approach motion for artificial hip joint replacements consisting of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup and a metallic or ceramic femoral head. A simple ball-in-socket configuration was adopted to represent the hip prosthesis for the lubrication analysis. Both the Reynolds equation and the elasticity equations were solved simultaneously for the lubricant film thickness and hydrodynamic pressure distribution as a function of the squeeze-film time was solved using the Newton-Raphson method. The elastic deformation of the UHMWPE cup was calculated by both the finite element method and a simple equation based upon the constrained column model. Good agreement of the predicted film thickness and pressure distribution was found between these two methods. A simple analytical method based upon the Grubin-Ertel-type approximation developed by Higginson in 1978 [1] was also applied to the present squeeze-film lubrication problem. The predicted squeeze-film thickness from this simple method was found to be remarkably close to that from the full numerical solution. The main design parameters were the femoral head radius, the radial clearance between the femoral head and the acetabular cup, and the thickness and elastic modulus for the UHMWPE cup; the effects of these parameters on the squeeze-film thickness generated in current hip prostheses were investigated.     

交联超高分子量聚乙烯人工髋关节磨损仿真模拟

人工髋关节超高分子量聚乙烯（UHMWPE）关节面磨损仍是影响置换关节远期寿命的主要因素,其仿真建模是对关节模拟机磨损测试手段的重要补充,也是实现置换关节临床前性能评估的有效方法。由多向运动产生的交叉剪切效应是影响UHMWPE磨损的主要原因之一,也是仿真建模的关键。现有理论方法将磨损深度确定为滑动距离的函数,并将90°交叉剪切运动条件下的磨损作为度量基准计算不同角度下的交叉剪切效应,但尚未考虑接触应力变量对磨损深度的影响。针对以上问题,提出了在垂直交叉剪切运动条件下将磨损深度表示为摩擦功函数的方法。该方法利用UHMWPE摩擦因数与接触压力的定量关系计算摩擦因数并确定摩擦功,解决了UHMWPE磨损交叉剪切效应中滑动距离与接触应力的耦合问题。基于磨损仿真新模型研究了36 mm直径的交联UHMWPE髋关节,并与已有ProSim模拟机试验结果进行了验证。结果显示该仿真模型可准确计算体积磨损和线性磨损等磨损量以及髋关节载荷方向改变对磨损的影响。磨损新模型为进一步仿真模拟奠定了有效基础。     

Contact mechanics analysis of metal-on-metal hip resurfacing prostheses

Finite-element method was employed to study the contact mechanics in metal-on-metal hip resurfacing prostheses, with particular reference to the effects of bone quality, the fixation condition between the acetabular cup and bone, and the clearance between the femoral head and the acetabular cup. Simple finite-element bone models were developed to simulate the contact between the articulating surfaces of the femoral head and the acetabular cup. The stresses within the bone structure were also studied. It was shown that a decrease in the clearance between the acetabular cup and femoral head had the largest effect on reducing the predicted contact-pressure distribution among all the factors considered in this study. It was found that as the clearance was reduced, the influence of the underlying materials, such as bone and cement, became increasingly important. Stress shielding was determined to occur in the bone tissue surrounding the hip resurfacing prosthesis considered in this study. However, the stress-shielding effects predicted were less than those observed in conventional total hip replacements. Both the effects of bone quality (reduction in elastic modulus) and the fixation condition between the cup and the bone were found to have a negligible effect on the predicted contact mechanics at the bearing surface. The loading was found to have a relatively small effect on the predicted maximum contact pressure at the bearing surface; this was attributed to an increase in contact area as the load was increased.     

Wear and deformation of ceramic-on-polyethylene total hip replacements with joint laxity and swing phase microseparation

Wear of polyethylene and the resulting wear debris-induced osteolysis remains a major cause of long-term failure in artificial hip joints. There is interest in understanding engineering and clinical conditions that influence wear rates. Fluoroscopic studies have shown separation of the head and the cup during the swing phase of walking due to joint laxity. In ceramic-on-ceramic hips, joint laxity and microseparation, which leads to contact of the head on the superior rim of the cup, has led to localized damage and increased wear in vivo and in vitro. The aim of this study was to investigate the influence of joint laxity and microseparation on the wear of ceramic on polyethylene artificial hip joints in an in vitro simulator. Microseparation during the swing phase of the walking cycle produced contact of the ceramic head on the rim of the polyethylene acetabular cup that deformed the softer polyethylene cup. No damage to the alumina ceramic femoral head was found. Under standard simulator conditions the volume change of the moderately crosslinked polyethylene cups was 25.6 +/- 5.3 mm3/million cycles and this reduced to 5.6 +/- 4.2 mm3/million cycles under microseparation conditions. Testing under microseparation conditions caused the rim of the polyethylene cup to deform locally, possibly due to creep, and the volume change of the polyethylene cup when the head relocated was substantially reduced, possibly due to improved lubrication. Joint laxity may be caused by poor soft tissue tension or migration and subsidence of components. In ceramic-on-polyethylene acetabular cups wear was decreased with a small degree of joint laxity, while in contrast in hard-on-hard alumina bearings, microseparation accelerated wear. These findings may have significant implications for the choice of fixation systems to be used for different types of bearing couples.     

Experimental Technique to Study Tangential-to-Normal Contact Load Ratio

This paper considers the mechanical interaction due to surface roughness and examines the surface theories using the classical definition of coefficient of friction: the tangential-to-normal load ratio. The postulation for maximum static friction is used to experimentally evaluate the contact models. For this purpose, a pin-on-disk test apparatus is employed with the capability of measuring tangential and normal forces for a frictional contact. The tests involve pairs of disks and specimens, that is, steel-on-steel and aluminum-on-aluminum contacts. In each case, profilometer measurements are performed on the disk and the Greenwood and Williamson parameters, are determined. Using the parameters, the theoretical estimates of normal and tangential loads are obtained. The theoretical values of tangential-to-normal contact load ratios are compared with those obtained from measurements for various applied normal loads. The tests utilizing a pin-on-disk apparatus showed a partial agreement between the experimentally obtained load ratios and the predicted upper limit confidence interval using the theoretical elastic and elastic-plastic contact. The result suggested that the elastic-plastic formulations provide better predictions of load ratios than the elastic contact formulations.     

Contact mechanics of metal-on-metal hip implants employing a metallic cup with a UHMWPE backing

The contact mechanics in metal-on-metal hip implants employing a cobalt chromium acetabular cup with an ultra-high molecular weight polyethylene (UHMWPE) backing were analysed in the present study using the finite element method. A general modelling methodology was developed to examine the effects of the interfacial boundary conditions between the UHMWPE backing and a titanium shell for cementless fixation, the coefficient of friction and the loading angle on the predicted contact pressure distribution at the articulating surfaces. It was found that the contact mechanics at the bearing surfaces were significantly affected by the UHMWPE backing. Consequently, a relatively constant pressure distribution was predicted within the contact conjunction, and the maximum contact pressure occurred towards the edge of the contact. On the other hand, the interfacial boundary condition between the UHMWPE backing and the titanium shell, the coefficient of friction and the loading angle were found to have a negligible effect on the contact mechanics at the bearing surfaces. Overall, the magnitude of the contact pressure was significantly reduced, compared with a similar cup without the UHMWPE backing. The importance of the UHMWPE backing on the tribological performance of metal-on-metal hip implants is discussed.     

Deformation of press-fitted metallic resurfacing cups. Part 2: Finite element simulation

The deformation of metallic acetabular cups employed for metal-on-metal hip resurfacing procedures was considered theoretically using the finite element method in the present study, following on the experimental investigation reported in Part 1. Three representative cups, characterized by the cup wall thickness as thin, intermediate, and thick, were considered. For the intermediate cup, the effects of both the size and the diametral interference on the cup deformation were investigated. Both two-dimensional axisymmetric and three-dimensional finite element models were developed to examine the important parameters during and after the press-fit procedure, and in particular the deformation of the metallic cup. The theoretical prediction of the cup deformation was in reasonable agreement with the corresponding experimental measurement reported in Part 1. The most significant factor influencing the cup deformation was the cup wall thickness. Both the size and the diametral interference were also shown to influence the cup deformation. It is important to ensure that the cup deformation does not significantly affect the clearance designed and optimized for tribological performances of metal-on-metal hip resurfacing prostheses. Furthermore the contact parameters at the cup and bone interface associated with the press fit were also discussed.     

Metal-on-metal hip joint tribology

The basic tribological features of metal-on-metal total hip replacements have been reviewed to facilitate an understanding of the engineering science underpinning the renaissance of these hard-on-hard joints. Metal-on-polymer hip replacements operate in the boundary lubrication regime, thus leading to the design guidance to reduce the femoral head diameter as much as is feasible to minimize frictional torque and volumetric wear. This explains why the gold-standard implant of this form from the past half-century had a diameter of only 22.225 mm (7/8 in). Metal-on-metal implants can operate in the mild mixed lubrication regime in which much of the applied load is supported by elastohydrodynamic films. Correct tribological design leads to remarkably low steady state wear rates. Promotion of the most effective elastohydrodynamic films calls for the largest possible head diameters and the smallest clearances that can reasonably be adopted, consistent with fine surface finishes, good sphericity and minimal structural elastic deformation of the cup on its foundations. This guidance, which is opposite in form to that developed for metal-on-polymer joints, is equally valid for solid (monolithic) metallic heads on metallic femoral stems and surface replacement femoral shells. Laboratory measurements of friction and wear in metal-on-metal joints have confirmed their potential to achieve a very mild form of mixed lubrication. The key lies in the generation of effective elastohydrodynamic lubricating films of adequate thickness compared with the composite roughness of the head and cup. The calculation of the film thickness is by no means easy, but the full procedure is outlined and the use of an empirical formula that displays good agreement with calculations based upon the full numerical solutions is explained. The representation of the lambda ratio, lambda, embracing both film thickness and composite roughness, is described.