EFFECTS OF NONLINEAR VISCOELASTIC MODELS OF CARTILAGE IN FINITE ELEMENT ANALYSIS OF KNEE JOINT

Abstract

Finite element analysis (FEA) of the biomechanics of the knee 
joint requires nonlinear material models for cartilage in cases 
of knees with unicompartmental osteoarthritis (UOA). We 
present the FEA of two nonlinear material models to describe 
the mechanical behavior of cartilage in cases of knees with 
unicompartmental osteoarthritis (UOA). The selected nonlinear material models consider finite deformations and 
nonlinear viscoelastic behavior over time. This work uses a 
generalized viscoelastic Maxwell model as well as hypo-type 
constitutive equations and a hyperelastic model of strain 
potential energy. Relaxation behavior is reproduced by using 
kernel functions for shear and volume relaxation, which are 
represented in terms of Prony series. The proposed material 
models are validated with experimental data of indentation 
tests of knee cartilage in cases of unicompartimental 
osteoarthritis, which were previously reported. For the 
reaction force the material models agree well in loading, 
relaxation and unloading for the viscohypoelastic (R2 = 0.974) 
and viscohyperelastic (R2 = 0.975) models. The 
viscohypoelastic cartilage versus linear elastic models are 
compared in a three-dimensional model of knee joint, results 
of this comparison showed a maximum difference up to 2.5 
times for contact areas, 1.5 times for axial displacement and 
1.6 times for von Mises stresses. Our findings suggest that 
viscoelastic behavior of cartilage in UOA can be well 
reproduced with a viscohypoelastic or a viscohyperelastic 
model. This nonlinear viscoelastic behavior modifies not only 
the structural response of cartilage but also can be useful in 
the design process of artificial unicompartmental prosthesis 
and to understand the degeneration and wear of the native 
cartilage left in the other compartment in cases of UOA.