Articular cartilage exhibits inhomogeneous, rate-dependent and tension-compression (TC) nonlinear material properties. The objective of this study was to assess the influence of TC nonlinearity on FE predictions of stress and strain as a function of congruency between two spherical cartilage layers. It was hypothesized that TC nonlinear and neo-Hookean constitutive models would yield a similar response when the cartilage layers were nearly congruent, but as the congruency of the cartilage layers decreased the predicted response from the two materials would be different.

Four FE models representing two spherical, contacting cartilage layers were created. The models had the same thickness (1.5 mm), but different radii (Fig. 1, panels A-C). The inner radius of the outer cartilage layer was a constant 26.5 mm. The outside radii of the inner cartilage layers were a ½, 3, 6, and 12 mm smaller than the inner radius of the larger cartilage layer, respectively. TC nonlinear and neo-Hookean constitutive equations were assigned to each of the congruency models. The coefficients for the TC constitutive equation were calculated from curve fits of fast-loading unconfined compression test data from four juvenile bovine knees. Shear moduli for the neo-Hookean models were chosen so that the load-displacement response of the neo-Hookean models were the same as the TC models for the same congruency and applied load (820 N).

The predicted pressures from neo-Hookean models were fairly uniform through the thickness regardless of model congruency (Fig. 1, panels A&B, both layers), while the TC nonlinear models predicted an increasing pressure gradient through the thickness as the models became more incongruent, with lower pressures at the contact surface (Fig. 1, panel D, inner layer). In contrast to the stress results, the circumferential strains were always higher for the neo-Hookean material and occurred at the contact surface. While there was essentially no difference in peak circumferential strains predicted by the two materials for the nearly congruent model, the neo-Hookean material predicted peak circumferential strains that were 20% higher than the TC nonlinear material for the incongruent model.

In conclusion, this research demonstrates that geometry has a substantial effect on a particular constitutive equations predicted mechanical response. In the context of modeling nearly concentric articular layers, there is very little difference between predictions obtained using a neo-Hookean model and the model with tension-compression nonlinearity. In contrast, when cartilage layers are not congruent, the effect of the tension-compression nonlinearity is significant.