Determination of nonlinear fibre-reinforced biphasic poroviscoelastic constitutive parameters of articular cartilage using stress relaxation indentation testing and an optimizing finite element analysis

An inverse method was developed to determine the material constitutive parameters of human articular cartilage from stress relaxation indentation tests. The cartilage was modeled as a fibre-reinforced nonlinear biphasic poroviscoelastic material, and a finite element (FE) model was used with a simulated annealing (SA) optimization algorithm to determine the material parameters that minimized the error between the experimental and predicted time dependant indentation loads. The values of the 15 optimized material parameters were found to be insensitive to the initial guesses, and, when friction between the indenter and the cartilage was considered, resulted in good agreement between the measured stress relaxation response and the FE prediction (R(2)=0.99). The optimized material parameters determined from experiments that used two different indenter sizes on the same samples were compared. When assuming frictionless contact between the indenter and the cartilage, all of the optimized parameters except for the Poisson's ratio were found to be relatively insensitive to indenter size. A second set of models that included frictional contact greatly reduced the sensitivity of the optimized Poisson's ratio to indenter size, thus confirming the validity of the model and demonstrating the importance of modeling friction. The results also demonstrate the robustness of the SA optimization algorithm to ensure convergence of a large number of material properties to a global minimum regardless of the quality of the initial guesses.