Several finite element analyses have focused on simulating the tissues and bones of the knee joint to study different pathologies that affect its natural functionality. A linear elastic behavior has been considered in recent studies for articular cartilage despite its viscoelastic nature. The aim of this work is to propose a viscoelastic material model that allows simulating its structural strength and the elastic strain energy that it absorbs per unit volume.For this, experimental data reported from flat cylindrical indentation test on human samples of seven patients with unicompartmental osteoarthritis (N=7) were used. These data allowed the adjustment of two non-linear material models, a visco-hypoelastic (VE) and a visco-hyperelastic (VHE) model, both models consider shear and volumetric relaxation phenomenon adjusted through Kernel functions for Prony series. The Arruda-Boyce model was used like the hyperelastic model. Fourteen finite element indentation models were performed, with the specific geometrical characteristics of cartilage thickness reported in the experimental tests. The PLANE183 element was used, which is a finite element with a high order bidimensional axisymmetric, through the commercial finite element software, ANSYS™. The models considered the indenter as a rigid body, the cartilage and subchondral bone as deformable bodies. The contact simulation in the bone-cartilage interface was generated through restriction equations allowing the simulation of the rigid contact between these tissues, while the contact in the indenter-cartilage interface was generated through contact elements with standard behavior which considers sliding between surfaces and separation between them. The contact algorithm to solve the contact phenomenon was the Augmented Lagrange Method. As boundary conditions, a displacement constraint in all directions on the subchondral bone and a displacement of 0.5mm in the axial direction of the indenter with a displacement ratio of 0.21mm/s were applied. The indentation force (F, material model structural reaction) and resilience modulus (Er, elastic strain energy per unit volume) were considered as validation parameters for the model and to compare with the experimental data.The results showed that the structural behavior of the material models and the fitted constants allow to reproduce the viscoelastic structural stiffness of the cartilage for the indentation force with a mean error of 4.43 ± 2.33% and 3.37 ± 1.03% for the VE and VHE model, respectively. For the elastic strain energy, Er, we obtain a mean error of 23.8 ± 13.27% for the VE and 19.05 ± 14.27% for the VHE model, respect to the experimental data.Results suggest that both proposed viscoelastic models can predict the structural stiffness and strain energy, however, the visco-hyperelastic non-linear model presents the lowest error for the numerical prediction of both the indentation force and the elastic strain energy per unit of volume.

A Comparison of Visco-Hypoelastic and Visco-Hyperelastic Model to Predict the Elastic Strain Energy for Articular Cartilage of Knee Joint

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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