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

1 - Compute the centre of the bottom and top endplate, and
+
2 - Compute the disc centre, = ( )/2
3 - Loop over the elements of the AF
.1 - Compute the position of the integration points for each element
.2 - Loop over the integration points, .1 - Computation of , Figure 1.b
.1 - Read and store the coordinates of the nodes which lay on the same plane (same
z-coordinate) for the internal and external surfaces, ± ∆z (e.g seed size)
.2 - Resampling of the points of the external and internal surfaces of the AF
.3 - Compute the temporary centre disc cross-section, .4 - Definition of sets of n points around on the external, , and internal
surfaces,
.5 - Definition of polynomial curves of order n (e.g. second order) by fitting over
the , , and the ,
.6 - Compute the line over and and its intersection with and ,
and .7 - Compute the vectors tangent at the intersection points, and
.8 - Compute the distance = | − | and = | − |
.9 - Determine = + − / .2 - Computation of , Figure 1.c
and ,
.1 - Compute the angle between x-axis and the line over the .2 - Rotation of of the AF elements to have aligned over x-axis
.3 - Selection of the nodes within a certain offset ± ∆y (e.g. seed size)
.4 - Repeat steps 3.2.1.4 – 9 using the instead of to determine
⁞
.10 - Determine by rotation of − of .3 - Determine = × .4 - Rotation of ± around of , where is the fibre angle with respect the
transversal plane, (30°). The sign of has to be chosen according to the number
of layers described and the relative position of in the AF. The rotated represents the fibre orientation at , fibre
.5 - Storing of the element number, the integration number and the fibre components.
4 - Write in a file the fibre orientation per integration point or per element (average and
normalization)
Box.1 Algorithm to compute fibre direction
homogeneous, slightly compressible material, = 0.45, Eq.(2). The embedded collagen
fibres were described by a polynomial formulation [2], Eq. (3). The material
components of the fibres have been modelled as reacting only to elongation.
(1) = ̅ − 3 +
− 1
(2) () = ̅ − 3 + ̅ − 3 +
( − 1)
(3) () =
/ /
− 1 − ln( ) ≥ 1 , 0 ℎ