Biomedical Engineering Reference
In-Depth Information
Ta b l e 1
KUBC: Kinematic uniform boundary conditions (3 kinematic constraints on each surface)
Load case
Top
Bottom
East
Wes t
North
South
x-tension
u
1
=
x
·
u
0
u
1
=
x
·
u
0
u
1
=
u
0
u
1
=
0
u
1
=
x
·
u
0
u
1
=
x
·
u
0
u
2
=
u
2
=
u
2
=
u
2
=
u
2
=
u
2
=
0
0
0
0
0
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
xy-shear
u
1
=
0
u
1
=
0
u
1
=
0
u
1
=
0
u
1
=
0
u
1
=
0
u
2
=
x
·
u
0
u
2
=
x
·
u
0
u
2
=
u
0
u
2
=
0
u
2
=
x
·
u
0
u
2
=
x
·
u
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
Ta b l e 2
PMUBC: Periodic mixed uniform boundary conditions (combination of kinematic and
stress constraints)
Load case
Top
Bottom
East
Wes t
North
South
x-tension
t
1
=
0
t
1
=
0
u
1
=
u
0
/
2
u
1
=−
u
0
/
2
t
1
=
0
t
1
=
0
t
2
=
0
t
2
=
0
t
2
=
0
t
2
=
0
u
2
=
0
u
2
=
0
u
3
=
0
u
3
=
0
t
3
=
0
t
3
=
0
t
3
=
0
t
3
=
0
xy-shear
t
1
=
0
t
1
=
0
t
1
=
0
t
1
=
0
u
1
=
u
0
/
2
u
1
=−
u
0
/
2
t
2
=
0
t
2
=
0
u
2
=
u
0
/
2
u
2
=−
u
0
/
2
t
2
=
0
t
2
=
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
u
3
=
0
Ta b l e 3
SUBC: Stress uniform boundary conditions (3 stress constraints on each surface)
Load case
Top
Bottom
East
Wes t
North
South
x-tension
t
1
=
0
t
1
=
0
t
1
=
t
0
/
2
t
1
=−
t
0
/
2
t
1
=
0
t
1
=
0
t
2
=
0
t
2
=
0
t
2
=
0
t
2
=
0
t
2
=
0
t
2
=
0
t
3
=
0
t
3
=
0
t
3
=
0
t
3
=
0
t
3
=
0
t
3
=
0
xy-shear
t
1
=
0
t
1
=
0
t
1
=
0
t
1
=
0
t
1
=
t
0
/
2
t
1
=−
t
0
/
2
t
2
=
0
t
2
=
0
t
2
=
t
0
/
2
t
2
=−
t
0
/
2
t
2
=
0
t
2
=
0
t
3
=
0
t
3
=
0
t
3
=
0
t
3
=
0
t
3
=
0
t
3
=
0
In principle, only an apparent solution can be expected. Fortunately, the boundary
cells, which cause discontinuity, become less important with increasing RVE size.
The apparent solution finally converges towards the effective solution [
15
]. However,
computer resources are limited and size is a very important factor. Doubling the RVE
size means eight-times more memory and tripling the RVE size even means 27-times
more memory. The stochastic distributed stiffness further reduces the efficiency of
common sparse-solver. For example, the calculation of six load cases needs about
2h on one core and 25min on six cores (each Xeon E7-4830) for a cube with 50
elements per edge. A simulation with 100 elements per edge runs 27h on 8 cores
and needs 100GB memory instead of 6.4GB for 50 elements per edge.
