Biomedical Engineering Reference
In-Depth Information
3 Results
3.1 Monte-Carlo Simulation
Figure
7
shows the sequence of aMonte-Carlo simulation for two different RVE sizes
of 20 and 50 elements. The Voigt and Reuss approximations converge separately. 50
elements per edge show a good agreement with only slight difference between both
approximations.
Figure
8
shows the associated probability plots of the individual moduli. Thereby,
the y-axis is scaled in a way that the values build a linear slope for a normal distri-
bution, which is in very good agreement for these kind of RVEs. It can be seen that
the graphs of the Voigt and Reuss approximations proceed closer for the larger RVE
size. The variance and the anisotropy error decrease for increasing RVE size. The
anisotropy error is 14.5% for a RVE size of 20 elements per edge and 3, 4% for a
RVE size of 50 elements. The numerical extra time of large RVE can obviously be
Fig. 7
Monte-Carlo simulation for RVE size of 20 (
left
) and 50 (
right
) elements per edge, respec-
tively
Fig. 8
Probability plot of the calculated Young's moduli for RVE size of 20 (
left
) and 50 (
right
)
elements per edge, respectively
