Biomedical Engineering Reference
In-Depth Information
Fig. 9
Influence of boundary conditions and window size.
Left
RVE window.
Right
Dependence
of the Young's modulus on number of elements per edge (window size) for varying boundary
conditions
compensated by a reduced number of necessary simulations. The normal distribution
allows to achieve an effective stiffness by averaging only few simulations.
3.2 RVE Size and Boundary Conditions
Figure
9
shows the convergence behavior of the three different sets of boundary
conditions for a RVE with 25% volume fraction and 0.2% initial cells. The Young's
moduli are plotted against the RVE size. Each modulus is the average of 48 sim-
ulations. Expectedly, the PMUBCs converge best. The effective modulus is nearly
obtained with a RVE size of 20 elements per edge, while the KUBCs and SUBCs
converge badly. These sets do not give effective moduli even for a RVE size of 120
elements per edge. As mentioned above, the KUBC estimates the structure too stiff,
whereas the SUBC estimates the structure too soft. The convergence study is stopped
at a RVE size of 120 elements per edge due to computational resources.
For further investigations, however, a RVE size of 50 elements per edge in com-
bination with PUMBCs is chosen and the isotropic elasticity moduli of 48 random
simulations are averaged, without rechecking for convergence.
3.3 Analysis of Stochastic Microstructures
Tables
4
-
6
and Fig.
10
present the results of three structure types with varying
percentage amount of initial cells (0.00625, 0.2 and 6.4%) for different volume
fractions. Thereby, the respective moduli are fitted with the following empirical
equation.
