Modeling of Creep and Stress Relaxation Behaviour of an Articular Carilage by Finite Element Method

Articular cartilage is a viscoelastic, soft, semitransparent tissue with an opalescent bluish tint, overlying the articulating bony surfaces in diarthrodial joints. It serves as the load-bearing material of joints, with excellent lubrication and wear characteristics. The elastic properties like young's modulus and visco elastic properties like Stress relaxation modulus and creep compliance of an articlular cartilage play a key role in determining its ability to bear and transmit the loads. Nanoindentation is being used extensively to measure the nanomechanical properties of hard thin films and small biological structures like living cells and biological tissues such as articular cartlage. Computational techniques such as Finite Element Method can also be used to extract elastic and visco elastic properties of such materials by modeling of nanoindentation. In this paper, an attempt is made to extract linear elastic and visco elastic properties (time dependent) of an articular cartilage by using Finite Element Modeling (FEM) of nanoindentation. Simulation has been carried out with the elastic modulus available from the literature as input. The load – displacement characteristic curves obtained from numerical simulation is compared with curves obtained from the experimental results available in the literature and the Hertz analytical results. A good correlation is found among the simulated results and experimental and analytical results. The displacement-time data and Load-time data for constant loading and constant displacement obtained by simulation is compared with the analytical results and a good agreement is found between the two in all the cases. Simulation has been done with a spherical indenter to analyze the time dependent deformation of the articular cartilage as a function of stress, strain and with in the 10% of thickness of the sample to avoid substrate influence.