Biomechanical Properties and Behaviours of the Wrist Joint - Computational Biomechanics of the Wrist Joint - page 21

2.4.2.5 Cartilage Modelling

The cartilage impacts the kinematics of the wrist joint due to its functions in
intermediating load transfer between bones. Several ways were found in previous
study in order to model the cartilage. Biphasic, transversely isotropic material
properties was one of the methods used [ 53 ]. It is however was less utilised as
compared to the less complex [ 57 ] linear elastic material properties [ 22 , 24 , 37 ,
54 - 56 ]. Additionally, there were more modelling methods that have been inves-
tigated; rigid body spring method, finite element method, Hertzian theory and an
elastic solution [ 57 ]. They found that the finite element method had the advan-
tages, which enable micromotion and stress distribution study to be performed
within the contacted bodies, including the cartilage layer. Regarding elastic
solution, hyperelastic material model has been chosen in previous studies to rep-
resent the cartilage [ 58 - 60 ]. Models can be classified as:
Neo-Hookean model [ 27 ]

W ¼ C 10 I 1 3 ð Þ ð 2 : 4 Þ

Mooney-Rivlin model [ 27 ]

W ¼ C 10 I 1 3 ð Þ +C 01 I 2 3 ð Þ ð 2 : 5 Þ

Polynomial form [ 27 ]

W ¼ X

N

Þ i Þ j C ij I 1 3 ð ð I 2 3 ð 2 : 6 Þ

i ¼ 0 ; j ¼ 0

Yeoh model [ 27 ]

W ¼ X

N

Þ i

C i0 I 1 3

ð ð 2 : 7 Þ

i ¼ 0

Ogden model [ 27 ]

W ¼ X

n

l i
a i

k a i 1 þ k a 2 þ k a 3 3 ð 2 : 8 Þ

i ¼ 1

where C ij , and l i , are material stiffness constants corresponding to Young's
modulus in linear material. Above models except from the Ogden are based on the
principle invariants and the strain energy function is depend on first and second
principle invariants, i.e. W = W(I 1 ,I 2 ) due to incompressibility. The Ogden
model is directly based on principle stretch ratios, k.