\(\renewcommand{\AA}{\text{Å}}\)

# compute stress/cartesian command

## Syntax

    compute ID group-ID stress/cartesian args

- ID, group-ID are documented in compute command

- args = argument specific to the compute style

    stress/cartesian args = dim1 bin_width1 dim2 bin_width2 keyword
      dim1 = x or y or z
      bin_width1 = width of the bin
      dim2 = x or y or z or NULL
      bin_width2 = width of the bin
      keyword = ke or pair or bond

## Examples

    compute 1 all stress/cartesian x 0.1 NULL 0
    compute 1 all stress/cartesian y 0.1 z 0.1
    compute 1 all stress/cartesian x 0.1 NULL 0 ke pair

## Description

Compute stress/cartesian defines computations that calculate profiles of the diagonal components of the local stress tensor over one or two Cartesian dimensions, as described in (Ikeshoji). The stress tensor is split into a kinetic contribution \(P^k\) and a virial contribution \(P^v\). The sum gives the total stress tensor \(P = P^k+P^v\). This compute obeys momentum balance through fluid interfaces. They use the Irving–Kirkwood contour, which is the straight line between particle pairs.

Added in version 15Jun2023: Added support for bond styles

This compute only supports pair and bond (no angle, dihedral, improper, or kspace) forces. By default, if no extra keywords are specified, all supported contributions to the stress are included (ke, pair, bond). If any keywords are specified, then only those components are summed.

## 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 \(L_1/b_1\).

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 considers particles crossing a set of planes, while stress/cartesian computes averages for a set of small volumes. Moreover, this compute computes the diagonal components of the stress tensor \(P_{xx}\), \(P_{yy}\), and \(P_{zz}\), while stress/mop/profile computes the components \(P_{ix}\), \(P_{iy}\), and \(P_{iz}\), where \(i\) is the direction normal to the plane.

More information on the similarities and differences can be found in (Ikeshoji).

## Restrictions

These computes calculate the stress tensor contributions for pair and bond forces only (no angle, dihedral, improper, or kspace force). It requires pairwise force calculations not available for most many-body pair styles.

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.

## Related commands

compute stress/atom, compute pressure, compute stress/mop/profile, compute stress/spherical, compute stress/cylinder

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