Description of depth-dependent nonlinear viscoelastic behavior for articular cartilage in unconfined compression

An optimized digital image correlation (DIC) technique was applied to investigate the depth-dependent nonlinear viscoelastic properties of articular cartilage and simultaneously the biphasic nonlinear viscoelastic relaxation model of cartilage was proposed and validated. The stress relaxation tests were performed with different strain levels and it is found that the initial stress and relaxed stress at any time increase with increasing strain levels. The depth-dependent strain of cartilage was obtained by analyzing the images acquired using the optimized DIC technique and moreover the inhomogeneous relaxation modulus distributions within the tissues were determined at different relaxation time points under strain of 11.35, 19.35 and 30% respectively. The strain rate dependent nonlinear stress and strain curves were obtained for articular cartilage through uniaxial compression tests. It is noted that the Young's modulus exhibits a slight increase near the cartilage surface, and then increases fast with depth and both the magnitude and the variation of the Young's modulus are affected by increasing strain rates. A biphasic nonlinear viscoelastic relaxation model was proposed to predict the depth-dependent relaxation behavior of cartilage under unconfined compression and the results show that there are good agreements between the experimental data and predictions.

► Cartilage's depth-dependent properties were investigated by DIC technique.
► A biphasic nonlinear viscoelastic relaxation model was proposed for cartilage.
► The inhomogeneous relaxation modulus increases obviously with cartilage depth.
► The Young's modulus increases slightly firstly and then increases fast with depth.
► The modulus' magnitude and variation increase with increasing strain rates.