Dear lammps users,

I wonder whether anyone has an idea on how to conduct stress analysis to granular materials while using the granualr package in LAMMPS. So far I can only think of using compute pair command to calculate the forces between particles, and then sum up all the inter-particle forces as the total inner force of the whole system, and then divide the total inner force by the analyzed area, say the area in x-y plane, as the stress perpendiculr to the x-y plane. Does this calculation method make sense ot is there any other command that I can use to analyze stress and strain for a granular material system in LAMMPS?

P.S. I want to analyze the stress-strain relationship at atomic scale by establish a molecular dynamics model in LAMMPS and the stress-strain relationship at a larger scale using the granular package in LAMMPS. Does anyone have any suggestions?

Thanks a lot!

Wenjuan

Dear Wenjuan,

I guess this is what you want

http://lammps.sandia.gov/doc/compute_stress_atom.html

this can calculate contact stress, and also kinetic stress ( take caution : it does not calculate on the fluctuating velocity).

Also look at pressure, mentioned in the documentation. Calculations can make more sense, if you keep in mind, stress is at the contacts and not in the particle.

Best wishes

Prashant

Wenjuan,

As Prashant said, stress in an assembly of sheared granules can easily be computed by the compute pressure command. There is a multitude of papers (over a decade of work), which analyze constitutive behavior in different flow regimes (dense to dilute rapid flows). I would suggest looking them over before re-computing this vast amount of work. There are many authors to look into, some notable(but by no means all) are Campbell, Silbert, Luding, Sundaresan, etc.

Keep in mind that the extending results from homogeneous shear to real flows in bounded systems is anything but trivial.

Dear Eric and Parashant,

Thank you both so much for helping me out. I really appreicate it.

I’ve got some other question about using the granular package in LAMMPS: what is the unit in the simulation if granular package is used? How to determine the values for Gamma_n, Gamma_t, and xmu, if mechnical properties of the simulated material are known, such as elastic modulus and posion’s ratio. I found some descriptions about how to determine Kn and Kt from elastic modulus and posion’s ratio on the official website (http://lammps.sandia.gov/doc/pair_gran.html), but there is no further informaiton abotu the other parameters in Hooke or Hertz model. Could you please help me by any chance?

Thanks a lot!

Wenjuan

Dear Wenjuan,

These answers you can find in any of the DEM modelling papers. One of which is

J. Sun, F. Battaglia, and S. Subramaniam. Hybrid two-fluid DEM simulation of gas-solid fluidized beds. *Journal of Fluid Engineering*, 129(11):1394–1403, November 2007. ( go through DEM section ) .

for information on units, please visit units section of lammps, its a user defined quantity.

Gamma_n is the dampening coeffecient for finding this you would need to determine the coeffecient of restitution of your contacts (defined as per standard literature) and estimate contact time . Its a route to dissaption of energy.

The documentation has information on tangential coeffecient from normal coeffecients. Friction is not related to elastic modulus and posion’s ratio, at least not explicitly.

Hope these are useful.

Best wishes

Prashant

Dear Prashant,

Thank you so much! All the information is very helpful. Appreciated!

Best regards,

Wenjuan

Wenjuan,

The ratio of spring constants in the elastic Hertzian model can be related to the poisson ratio(I believe you can even find that in a wiki page, if not it should be readily accessible from a quick lit. search.) Dissipation has no real standard model, or for that matter a rigorous basis from a coarse graining point of view. Look up Colin Thornton’s papers if you would like to see a few paths to deriving dissipative models.

That being said, different models have different advantages. From a kinetic theory standpoint, which is useful for dilute flows, the linear spring dash-pot model allows for clean treatment as it yields a constant coefficient of restitution(CoR). On the other hand, the Kono-Kuwabara model (Hertzian with nonlinear damping found in lammps) is often used because force ->0 as overlap -> 0, and it reproduces experimental trends in the CoR for materials with linear elasticity.

In any case you won’t be able to simulate realistically hard materials as the time step will get prohibitively small, so get a handle on the non-dimensional parameters of interest for these problems.

Dear Eric,

Thank you so much for your suggestions. Appreciated!

Best regards,

Wenjuan