# Per atom stress formulation

Dear all,

I was wondering if someone could clarify the formulation of “per atom stress” in the documentation (page http://lammps.sandia.gov/doc/compute_stress_atom.html):

1. why is the kinetic energy term not divided by 2?
2. the summation is written such that the sum runs from n=1, however, inside the sum, there is no n, but (r1aF1b + r2aF2b) instead, I am not quite sure how to interpret this…

Is there a paper/link on how the per atom stress calculation is performed in LAMMPS?

Thank you very much in advanced!

With best wishes,
Anna

Dear Anna,

I suppose the kinetic energy term is m*v_a*v_b/2 + m*v_b*v_a/2

The sums are explained in the paragraph following the formula.

Regards,
Oleg.

20.11.2013, 18:26, "Anna Lappala" <[email protected]...>:

Sorry, what I wrote about kinetic energy term was wrong. Should not answer before thinking It has such form because it is the transfer of a-component of momentum along b direction. Look e.g. Heinz, Mol. Sim. 33 (2007).

Oleg.

20.11.2013, 18:37, "Oleg Sergeev" <[email protected]...>:

1. the summation is written such that the sum runs from n=1, however, inside the sum, there is no n, but (r1aF1b + r2aF2b) > > instead, I am not quite sure how to interpret this…

The doc page says:
The second term is a pairwise energy contribution where n loops over the Np neighbors of atom I, r1 and r2 are the positions of the 2 atoms in the pairwise interaction, and F1 and F2 are the forces on the 2 atoms resulting from the pairwise interaction.

Is there a paper/link on how the per atom stress calculation is performed in LAMMPS?

yes, see the paper by Aidan Thompson (lead author) on the LAMMPS citation page, in J Chem Phys.

Steve

Dear Steve,

Thank you, so if I understand correctly, to keep the n inside the sum formulation what one has to say is r_n_a*F_n_b + r_(n+1)_a*F_(n+1)_b? The n has to be in the sum somehow, because otherwise it does not seem to make sense mathematically, as the sum goes from n=1, but n is not in the summation itself...

Thanks,
Anna

Dear Oleg,

I do not have access to this paper- could you possibly send me a PDF of it?

Thanks,
Anna

Sent off-list.

Oleg

20.11.2013, 19:53, "Anna Lappala" <[email protected]...>:

It’s not meant to be a precise mathematical formula. As the text states, it’s just a sum
over neighbors of atom I and R1 and R2 are the coords of I and J, the 2 atoms
in the pairwise interaction.

Steve