1. Input
The allow inputs for this version of the tool includes: number of particles, volume fraction of material A,
Young’s modulus and Poisson’s ratio of material A and B, and a Boolean checking whether to use nonlocal
formulation or not. The number of particles is given by the size of the die that the user chooses. Since the
solver does not generate the configuration of the initial powder bed (random close packing), we provide 3
pre-determined powder bed and each has 129, 341 and 717 particles, respectively. We give the complete
freedom of the value of the Young’s modulus of material A to the user, but restrict Young’s modulus of B
within a range from 0.01 to 100 times the modulus of A. The reason for this is that if the difference between
the modulus of the two materials is too large, which means one is too soft compared to the other, this
becomes a soft-hard mixture and it requires another model to deal with. Similar reason for why we restrict
the Poisson’s ratio of both materials to below 0.45. The system is very incompressible as the Poisson’s ratio
approaches 0.5 and another model is needed to deal with this situation. We will allow the user to choose
whether to use nonlocal contact formulation or not. If no, then the simulation will be based on Hertz theory
and the max relative density will be 1; if yes, then it will be based on nonlocal contact formulation and the
max relative density will be 0.9. The reason is that at a very high relative density, using nonlocal contact
formulation to solve the system will take too much effort. So for the purpose of this application, we restrict
it to below 0.9. Switch between these two theories, the user will be able to see the differences in the
simulation results. The results are not very different at lower relative density (0.55 to 0.65), but start to
deviate more and more as the relative density increases from 0.65.
Table 1: Detailed configurations of the initial powder beds
Container No.
NLC
NP
DR
DH
MaxRD
TOL
Number of cores
Wall time (16 cores)
Force distr. (PP)
Force distr. (PW)
1
0
129
1.5e-3
1.97e-3
1
5.0e-7
2
200 hrs
TBD
TBD
2
0
341
2e-3
2.52e-3
1
5.0e-7
4
300 hrs
15
5
3
0
717
2.5e-3
3.27e-3
1
5.0e-7
8
300 hrs
30
10
1
1
129
1.5e-3
1.97e-3
0.9
5.0e-7
2
200 hrs
TBD
TBD
2
1
341
2e-3
2.52e-3
0.9
5.0e-7
4
300 hrs
15
5
3
1
717
2.5e-3
3.27e-3
0.9
5.0e-7
8
300 hrs
30
10
2. Outputs
The displayed outputs include: compaction plot 1 (pressure vs. relative density), compaction plot 2(pressure
vs. height), mean coordination number evolution, contact force distribution and 3D visualization of the
powder bed evolution. Compaction plot 1 and 2, similar to that in figure 5, contain pressure from the upper
and lower punch and from the die wall, separately. The user will notice that the pressures from the upper
and lower punch are exactly the same. The plot of mean coordination number versus relative density will
vary between using nonlocal contact formulation and not using it. Since at high level of confinement (high
relative density), contacts cannot be assumed to be independent and contacts may form or break due to the
effect of other contact forces. By mean coordination number, we mean the average number of particles that
are in contact with a single particle. This number increases as the relative density rises, one particle starts
to interact with more particles as the system gets compressed and this number is very sensitive to the
compressibility of the system when using the nonlocal contact formulation, but not very sensitive if Hertz
theory is used. We provide the force distribution evolution of both particle-particle interaction and particlewall interaction. The results will show that as the relative density increases, the force distribution curve of
particle-particle interactions will deviate from that of the particle-wall interactions. In the 3D powder bed
evolution, we provide the visualization of how the system reacts under compression and we also provide
the option to see only one kind of material, so the user will be able to look into the system.
3. Graphic interface and flow of the tool
Figure 1: graphic user interface
This is the user interface of the tool, with input window on the left and a brief explanation of the function
and capability of the tool on the right. The tool first opens a tool.xml file when it gets launched, which
defines the features of the GUI. When the user finishes entering input values and clicks simulate button, a
main_input.m file will take all the inputs and save them in .dat files. Then a gscompaction.py script file will
deploy all the .dat files and submit simulation job on Purdue cluster conte. The results will be returned in
the form of .txt files which will be retrieved by main_output.m file. This file will perform all the postprocessing and generate and save graphical outputs back to the GUI. The compaction plot 1 and 2 are
created by plotting pressure at the upper punch, lower punch and the reaction at the die wall against the
relative density and the height of the tablet, respectively.
Figure2: compaction plot 1 (pressure vs. relative density), 341 particles, Hertz theory
Figure3: compaction plot 2 (pressure vs. height), 341 particles, Herts theory
For the mean coordination number plot, we take the average of the number of particles that are in contact
with a single particle at each loading step and plot it against the relative density. For the contact force
distribution plot, we use the ratio between the force on each particle and the average contact force in the
system as the x-axis and plot the probability in log scale, with red representing particle-particle interaction
and blue representing particle-wall interaction.
Figure4: mean coordination number evolution, 341 particles, Hertz theory
Figure5: contact force distribution, 341 particles, Hertz theory, at relative density of 0.61751
Figure6: contact force distribution, 341 particles, Hertz theory, at relative density of 1.0086
In the 3D powder bed evolution, we applied unstructured mesh in the sequence display. The mesh points
in space are the positions of each particle in the system and we used the diameter of the particle as the field
values at each mesh points. The mesh points change with respect of the relative density, but the field values
do not. So when we put all the unstructured meshes together, filled with field values of the diameter, in a
sequence with respect to the relative density, we create a 3D animation of the powder bed evolution.
Figure7: 3D powder bed evolution, 0.75 volume fraction of material A, 717 particles, Hertz theory, at relative density of 0.601
Figure8: 3D powder bed evolution, 0.75 volume fraction of material A, 717 particles, Hertz theory, at relative density of 1.0116
Below is an illustration of tool flow at the back stage.
Figure9: tool flow
4. Suggestions for future versions
In the expected future versions of the tool, the user will be given more control on the input. The solver does
not provide the initial powder beds, so we may let the user to upload their own initial powder bed for
simulation. We may also give the user the freedom to enter the radius of the particles within a given range,
since if the particles are too small, especially at nano-level, the governing physics is different from that in
the micro level. In the current version, only elastic deformation is considered, but the solver is able to deal
with more physical mechanisms, like hyper-elastic and plastic deformation. So we may open these
mechanisms and the tool will be able to deal with more situations. We may provide the option to simulate
the behavior of only one particle under compaction. This is a relatively easier experiment to perform, so
the user can compare the experimental data and the simulation results from the tool. If it’s accurate enough,
we can provide the simulation on the behavior of a system of that single particle. The assumption of monodisperse system might be removed, so the particles do not have to be the same size; and they may have
irregular shape, instead of just spheres. As we remove more and more assumptions, the simulation will
approach the real situation closer and closer.