Depth and rate dependent mechanical behaviors for articular cartilage: Experiments and theoretical predictions

• Cartilage's depth-dependent creep strain and compliance were investigated.
• Young's modulus increases along cartilage depth and with increase of stress rate.
• Poisson's ratio increases along cartilage depth.
• Depth-dependent nonlinear viscoelastic constitutive model of cartilage was built.

An optimized digital image correlation (DIC) technique was applied to investigate the depth-dependent mechanical properties of articular cartilage and simultaneously the depth-dependent nonlinear viscoelastic constitutive model of cartilage was proposed and validated. The creep tests were performed with different stress levels and it is found that the initial strain and instantaneous strain increase; however the creep compliance decreases with the increase of compressive stress. The depth-dependent creep strain of cartilage was obtained by analyzing the images acquired using the optimized DIC technique. Moreover the inhomogeneous creep compliance distributions within the tissues were determined at different creep time points. It is noted that both creep strain and creep compliance with different creep times decrease from cartilage surface to deep. The depth-dependent creep compliance increases with creep time and the increasing amplitude of creep compliance decreases along cartilage depth. The depth-dependent and stress rate dependent nonlinear stress and strain curves were obtained for articular cartilage through uniaxial compression tests. It is found that the Young's modulus of cartilage increases obviously along cartilage depth from superficial layer to deep layer and the Young's modulus of different layers for cartilage increases with the increase of stress rate. The Poisson's ratio of cartilage increases along cartilage depth with given compressive strain and the Poisson's ratio of different layers decreases with the increase of compressive strain. The depth-dependent nonlinear viscoelastic constitutive model was proposed and some creep data were applied to determine the parameters of the model. The depth-dependent compressive behaviors of cartilage were predicted by the model and the results show that there are good agreements between the experimental data and predictions.