ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

The growth laws for a day, adopted from Fickin et al., (2009), are applied to the
reference or pre growth configuration where the growth occurs at the stress free state.
The mechanical loading is then applied to the post growth configuration and this cycle
repeats for number of days.
Table 1 Parameters for hyperelastic stress constitutive equations of proteoglycans and collagens (Ficklin
et al., 2009).
(MPa)
0.046
2.02
(MPa)
0.11
(MPa)
0.53
(MPa)
0.53
(MPa)
0.27
Table 2 Volume fractions and material constants, Ficklin et al., (2009)
(MPa)
0.53
(deg)
45
(deg)
45
(deg)
Volume fractions
Permeability,
, Metal implant
/
M
Young’s
, GPa
modulus, Poisson
ratio,
0.886 0.064 0.014 0.036 2.46 10 8.88 35 0.3
The Cauchy and second Piola-Kirchhoff stress tensors (denoted by and , respetively)
are related by
, 2
where , is scalar strain energy function, is right Cauchy-
Green deformation tensor.
The strain energy functions (Ficklin et al., 2009) are
1 1
6
1 1 1
1 1 1
where ,,,,, represent the square of the stretch of the material
line element, ,,, are material constants that represent bimodular terms as
0 1 otherwise 0.
4. IMPLEMENTATION IN COMSOL
A simplified 2D axisymmetric representation of femoral cartilage of the human knee
joint was reproduced from Wilson et al., (2003). The geometry was modified to include
a defect sized (diameter 10 mm) metal implant (Fig. 2). The implant was placed slightly
sunk (30% of cartilage thickness) into the cartilage with the surface of the implant
perfectly matching the articulating surface. The hyperelastic constitutive equations for
constituents (PG’s and COL) are implemented using solid mechanics module. The fluid
flow equations are included through Darcy law module. These two physics are coupled
manually through equations. The models were solved with and without considering the
defect sized implant.
45