LAMMPS Polydisperse Packings
Random polydisperse spherical packings can be generated by randomly placing spheres of different sizes into a box until no more will fit. While this sounds fairly straightforward, its not something that I want to invest time doing myself. Fortunately for me, a free and open source software package called LAMMPS, which is normally used for molecular dynamics simulations, can be used to create these packed systems. In this article I explain how this can be done.
LAMMPS Installation
Since this project only requires a basic build of LAMMPS, compiling from source is relatively simple. Download the source from their webpage and execute the following commands in the corresponding directories.
path/to/lammps/src/STUBS> make
path/to/lammps/src> make yes-granular
path/to/lammps/src> make serial
This will build a simple version of lammps with the optional granular package right in the directory. Note, this worked for me on mac OS X 10.10 and should be similar for linux.
LAMMPS Script
LAMMPS runs by reading in a script and executing the commands. I got the idea for using LAMMPS from another blog post. However, his scripts are intended for a dated version of LAMMPS, so I have posted my versions where I have made a few changes. The basic idea of the script is to periodically “pour” spheres into the top of the system and let them fall to the bottom. Interestingly, a quadratic potential is used for the pairwise interactions so they’re not technically hard sphere. However, this allows one to use a straightforward molecular dynamics simulation with gravity turned on to do the packing.
atom_style sphere
boundary p p fm
newton off
comm_modify vel yes
region reg block 0 1 0 1 0 1 units box
create_box 1 reg
neighbor 0.2 bin
neigh_modify delay 0
pair_style gran/hooke/history 200.0 NULL 50.0 NULL 0.5 0
pair_coeff * *
timestep 0.001
fix 1 all nve/sphere
fix 2 all gravity 1.0 spherical 0.0 -180.0
fix zlower all wall/gran 200.0 NULL 50.0 NULL 0.5 0 &
zplane 0.0 200.0
region slab block 0 1 0 1 0.5 1 units box
fix ins1 all pour 500 1 12345 region slab diam one 0.2
dump 1 all custom 100 dump.lmp type x y z radius
run 1000
Theres a lot going on here, but the most important line is the “fix pour” command. This command tells LAMMPS to insert 500 particles with diameter 0.2 into the system. For polydisperse systems, replace this line with the below “fix pour” command. This will insert particles with diameter 0.1 with 75% probability and diameter 0.2 with 25% probability.
fix ins1 all pour 500 1 12345 region slab diam poly 2 0.1 0.75 0.2 0.25
The “dump” command details data output (every 100 time steps) and format (type x y z rad). The last command actually runs the simulation. For a fully packed system, you will probably need to run for many more time steps (>100000). Note that you may not actually be able to fit 500 particles. The script is run with the following command.
path/to/lammps/src/lmp_serial -in script_file
Visualization
For visualization, I used software called OVITO, which is excellent and free. Thanks to Joel Berry for introducing this to me. It interfaces very nicely with LAMMPS. Just load the dump file using OVITO’s “LAMMPS Text Dump File” format option. Below is a small animation I created in OVITO of the simulation in action.
讨论：
Hi Ryan, I have a quick question:
I get: ERROR: Lost atoms: original 500 current 449 (../thermo.cpp:427) at timestep 0. I’m assuming that you put in an ignore statement as these lost atoms are due to them not fitting in the domain?
Many thanks again
Brani
(PS. cool blog, hope your PhD is going swell)
Yeah, this is a common error, I get it too. Its correct that not all particles will fit. But, I think the error is due to particles getting too close together (overlapping), creating a very large force that can’t be dealt with, and so Lammps removes those particles from the system. For packing systems, this shouldn’t be a big issue, but I would try visualizing the system to confirm that it is sufficiently packed. Ovito is visualization software that is free and great for this application, VMD will work as well.
Your post is very interesting and helpful.
I have a question for poly-disperse(more than 2) system.
For example, I modified input file of 3 type particle system as,
fix ins1 all pour 1000 1 12345 region slab diam poly 3 0.05 0.50 0.1 0.25 0.2 0.25.
(0.05~50%, 0.1~25%, 0.2~25%)
but, this input file brought error.
Is my input file is right?
Glad you found it helpful. I’ve never tried running with 3 different particle sizes, but your command looks correct according to the Lammps documentation. Perhaps there is an error elsewhere in your file. Also, make sure you have the granular package installed. It does not install by default and the script will not work without it.