Assessment of the applicability of the Hertzian contact theory to edge-loaded prosthetic hip bearings

Abstract

The components of prosthetic hip bearings may experience in-vivo subluxation and edge loading on the acetabular socket as a result of joint laxity, causing abnormally high, damaging contact stresses. In this research, edge-loaded contact of prosthetic hips is examined analytically and experimentally in the most commonly used categories of material pairs. In edge-loaded ceramic-on-ceramic hips, Hertzian contact theory yields accurate (conservatively, <10% error) predictions of the contact dimensions. Moreover, Hertzian theory successfully captures slope and curvature trends in the dependence of contact patch geometry on the applied load. In an edge-loaded ceramic-on-metal pair, a similar degree of accuracy is observed in the contact patch length; however, the contact width is less accurately predicted due to the onset of subsurface plasticity, which is predicted for loads >400 N. Hertzian contact theory is shown to be ill-suited to edge-loaded ceramic-on-polyethylene pairs due to polyethylene’s nonlinear material behavior. This work elucidates the methods and the accuracy of applying classical contact theory to edge-loaded hip bearings. The results help to define the applicability of Hertzian theory to the design of new components and materials to better resist severe edge loading contact stresses.

Do Obesity and/or Stripe Wear Increase Ceramic Liner Fracture Risk? An XFEM Analysis

“…A previously developed and physically validated [12] FE model of the overall THA construct was used for the global analysis. The computational zoning for the global model had been optimized for bearing contact and edge-loading [9] and had been validated by comparison with a corresponding Hertzian analytical contact stress solution reported by Sanders and Brannon [32].…”

Prediction of contact mechanics in metal-on-metal Total Hip Replacement for parametrically comprehensive designs and loads

“…3). Edge loading predictions were validated against data reported by Sanders and Brannon (2011) for 36 mm MoM hip implants (Fig. 3), and indicated predictions within 13.8% and 6.3% of semi-minor and semi-major axes respectively.…”

“…Polar loading was validated with three indicated head diameters and 10 mm diametral clearance. Edge loading was validated with two available MoM results for which the head diameter was 36 mm (Sanders and Brannon, 2011). θ Corresponded to the two edge loading positions used by Sanders and Brannon such that θ of 15°and 30°approximately equaled P F of 0.17 and 0.33, respectively.…”

“…5). Hence, designs with larger rim radii or compound radii as in some ceramic designs (Mak et al, 2011;Sanders and Brannon, 2011), may substantially reduce the wear challenge of transitional contact conditions. Permanent deformation was observed on the head and the cup rim.…”

A new shoulder model with a biologically inspired glenohumeral joint

“…Nevertheless, the current study is not without limitations that must be addressed. force developed in the contact between the humeral head and the glenoid cavity is modelled by the Hertz contact law, which assumes the contacting materials to be homogeneous, linear elastic, and isotropic [48] . In other words, its applicability to the GH joint is limited because it does not take into account the viscoelastic nature of the biological joints [49] .…”