$$\renewcommand{\AA}{\text{Å}}$$

# compute stress/spherical command¶

## Syntax¶

compute ID group-ID style args

• ID, group-ID are documented in compute command

• style = stress/cartesian or stress/spherical or stress/cylinder

• args = argument specific to the compute style

stress/cartesian args = dim bin_width
dim = x or y or z
bin_width = width of the bin
one or two dim/bin_width pairs may be appended
stress/cylinder args = zlo zh Rmax bin_width keyword
zlo = minimum z-boundary for cylinder
zhi = maximum z-boundary for cylinder
Rmax = maximum radius to perform calculation to
bin_width = width of radial bins to use for calculation
keyword = ke (zero or one can be specified)
ke = yes or no
stress/spherical
x0, y0, z0 = origin of the spherical coordinate system
bin_width = width of spherical shells
Rmax = maximum radius of spherical shells

## Examples¶

compute 1 all stress/cartesian x 0.1
compute 1 all stress/cartesian y 0.25 z 0.1
compute 1 all stress/cylinder -10.0 10.0 15.0 0.25
compute 1 all stress/cylinder -10.0 10.0 15.0 0.25 ke no
compute 1 all stress/spherical 0 0 0 0.1 10


## Description¶

Compute stress/cartesian, compute stress/cylinder, and compute stress/spherical define computations that calculate profiles of the diagonal components of the local stress tensor in the specified coordinate system. The stress tensor is split into a kinetic contribution $$P^k$$ and a virial contribution $$P^v$$. The sum gives the total stress tensor $$P = P^k+P^v$$. These computes can for example be used to calculate the diagonal components of the local stress tensor of interfaces with flat, cylindrical, or spherical symmetry. These computes obeys momentum balance through fluid interfaces. They use the Irving–Kirkwood contour, which is the straight line between particle pairs.

The stress/cartesian computes the stress profile along one or two Cartesian coordinates, as described in (Ikeshoji). The compute stress/cylinder computes the stress profile along the radial direction in cylindrical coordinates, as described in (Addington). The compute stress/spherical computes the stress profile along the radial direction in spherical coordinates, as described in (Ikeshoji).

## Output info¶

The output columns for stress/cartesian are the position of the center of the local volume in the first and second dimensions, number density, $$P^k_{xx}$$, $$P^k_{yy}$$, $$P^k_{zz}$$, $$P^v_{xx}$$, $$P^v_{yy}$$, and $$P^v_{zz}$$. There are 8 columns when one dimension is specified and 9 columns when two dimensions are specified. The number of bins (rows) is $$(L_1/b_1)(L_2/b_2)$$, where $$L_1$$ and $$L_2$$ are the lengths of the simulation box in the specified dimensions and $$b_1$$ and $$b_2$$ are the specified bin widths. When only one dimension is specified, the number of bins (rows) is $$L_1/b_1$$.

The default output columns for stress/cylinder are the radius to the center of the cylindrical shell, number density, $$P^k_{rr}$$, $$P^k_{\phi\phi}$$, $$P^k_{zz}$$, $$P^v_{rr}$$, $$P^v_{\phi\phi}$$, and $$P^v_{zz}$$. When the keyword ke is set to no, the kinetic contributions are not calculated, and consequently there are only 5 columns: the position of the center of the cylindrical shell, the number density, $$P^v_{rr}$$, $$P^v_{\phi\phi}$$, and $$P^v_{zz}$$. The number of bins (rows) is $$R_\text{max}/b$$, where $$b$$ is the specified bin width.

The output columns for stress/spherical are the position of the center of the spherical shell, the number density, $$P^k_{rr}$$, $$P^k_{\theta\theta}$$, $$P^k_{\phi\phi}$$, $$P^v_{rr}$$, $$P^v_{\theta\theta}$$, and $$P^v_{\phi\phi}$$. There are 8 columns and the number of bins (rows) is $$R_\text{max}/b$$, where $$b$$ is the specified bin width.

This array can be output with fix ave/time,

compute p all stress/cartesian x 0.1
fix 2 all ave/time 100 1 100 c_p[*] file dump_p.out mode vector


The values calculated by this compute are “intensive”. The stress values will be in pressure units. The number density values are in inverse volume units.

NOTE 1: The local stress does not include any Lennard-Jones tail corrections to the stress added by the pair_modify tail yes command, since those are contributions to the global system pressure.

NOTE 2: The local stress profiles generated by these computes are similar to those obtained by the method-of-planes (MOP). A key difference is that compute stress/mop/profile <compute_stress_mop> considers particles crossing a set of planes, while stress/cartesian computes averages for a set of small volumes. More information on the similarities and differences can be found in (Ikeshoji).

## Restrictions¶

These computes calculate the stress tensor contributions for pair styles only (i.e., no bond, angle, dihedral, etc. contributions, and in the presence of bonded interactions, the result will be incorrect due to exclusions for special bonds) and requires pairwise force calculations not available for most many-body pair styles. Note that $$k$$-space calculations are also excluded.

These computes are part of the EXTRA-COMPUTE package. They are only enabled if LAMMPS was built with that package. See the Build package doc page for more info.

## Default¶

The keyword default for ke in style stress/cylinder is yes.

(Ikeshoji) Ikeshoji, Hafskjold, Furuholt, Mol Sim, 29, 101-109, (2003).