Simulation of high tensile Poissonʹs ratios of articular cartilage with a finite element fibril-reinforced hyperelastic model

Analyses with a finite element fibril-reinforced hyperelastic model were undertaken in this study to simulate high tensile Poissonʹs ratios that have been consistently documented in experimental studies of articular cartilage. The solid phase was represented by an isotropic matrix reinforced with four sets of fibrils, two of them aligned in orthogonal directions and two oblique fibrils in a symmetric configuration respect to the orthogonal axes. Two distinct hyperelastic functions were used to represent the matrix and the fibrils. Results of the analyses showed that only by considering non-orthogonal fibrils was it possible to represent Poissonʹs ratios higher than one. Constrains in the grips and finite deformations played a minor role in the calculated Poissonʹs ratio. This study also showed that the model with oblique fibrils at 45° was able to represent significant differences in Poissonʹs ratios near 1 documented in experimental studies. However, even considering constrains in the grips, this model was not capable to simulate Poissonʹs ratios near 2 that have been reported in other studies. The study also confirmed that only with a high relation between the stiffness of the fibers and that of the matrix was it possible to obtain high Poissonʹs ratios for the tissue. Results suggest that analytical models with a finite number of fibrils are appropriate to represent main mechanical effects of articular cartilage.