Assessment of common hyperelastic constitutive equations for describing normal and osteoarthritic articular cartilage

With the aim of providing information for modelling joint and limb systems, widely available constitutive hyperelastic laws are evaluated in this paper for their ability to predict the mechanical responses of normal and osteoarthritic articular cartilage. Load-displacement data from mechanical indentation were obtained for normal and osteoarthritic cartilage at 0.1 s(-1) and 0.025 s(-1) and converted to the stress-stretch ratio. The data were then fitted to the Arruda-Boyce, Mooney-Rivlin, neo-Hookean, Ogden, polynomial, and Yeoh hyperelastic laws in the MATLAB environment. Although each of the hyperelastic laws performed satisfactorily at the higher rate of loading, their ability to fit experimental data at the lower loading rate varied considerably. For the preferred models, coefficients were provided for stiff, soft, and average tissues to represent normal and degraded tissue at high and low loading rates. The present authors recommend the use of the Mooney-Rivlin or the Yeoh models for describing both normal and degraded articular cartilage, with the Mooney-Rivlin model providing the best compromise between accuracy and required computational power.