\(\renewcommand{\AA}{\text{Å}}\)

fix indent command

Syntax

fix ID group-ID indent K gstyle args keyword value ...

• ID, group-ID are documented in fix command

• indent = style name of this fix command

• K = force constant for indenter surface (force/distance^2 units)

• gstyle = sphere or cylinder or cone or plane

  sphere args = x y z R
    x, y, z = position of center of indenter (distance units)
    R = sphere radius of indenter (distance units)
    any of x, y, z, R can be a variable (see below)
  cylinder args = dim c1 c2 R
    dim = x or y or z = axis of cylinder
    c1, c2 = coords of cylinder axis in other 2 dimensions (distance units)
    R = cylinder radius of indenter (distance units)
    any of c1,c2,R can be a variable (see below)
  cone args = dim c1 c2 radlo radhi lo hi
    dim = x or y or z = axis of cone
    c1, c2 = coords of cone axis in other 2 dimensions (distance units)
    radlo,radhi = cone radii at lo and hi end (distance units)
    lo,hi = bounds of cone in dim (distance units)
    any of c1, c2, radlo, radhi, lo, hi can be a variable (see below)
  plane args = dim pos side
    dim = x or y or z = plane perpendicular to this dimension
    pos = position of plane in dimension x, y, or z (distance units)
    pos can be a variable (see below)
    side = lo or hi

• zero or more keyword/value pairs may be appended

• keyword = side or units

  side value = in or out
    in = the indenter acts on particles inside the sphere or cylinder or cone
    out = the indenter acts on particles outside the sphere or cylinder or cone
  units value = lattice or box
    lattice = the geometry is defined in lattice units
    box = the geometry is defined in simulation box units

Examples

fix 1 all indent 10.0 sphere 0.0 0.0 15.0 3.0
fix 1 all indent 10.0 sphere v_x v_y 0.0 v_radius side in
fix 2 flow indent 10.0 cylinder z 0.0 0.0 10.0 units box

Description

Insert an indenter within a simulation box. The indenter repels all atoms in the group that touch it, so it can be used to push into a material or as an obstacle in a flow. Alternatively, it can be used as a constraining wall around a simulation; see the discussion of the side keyword below.

The gstyle keyword selects the geometry of the indenter and it can either have the value of sphere, cylinder, cone, or plane.

A spherical indenter (gstyle = sphere) exerts a force of magnitude

\[F(r) = - K \left( r - R \right)^2\]

on each atom where K is the specified force constant, r is the distance from the atom to the center of the indenter, and R is the radius of the indenter. The force is repulsive and F(r) = 0 for r > R.

A cylindrical indenter (gstyle = cylinder) follows the same formula for the force as a sphere, except that r is defined the distance from the atom to the center axis of the cylinder. The cylinder extends infinitely along its axis.

Added in version 17April2024.

A conical indenter (gstyle = cone) is similar to a cylindrical indenter except that it has a finite length (between lo and hi), and that two different radii (one at each end, radlo and radhi) can be defined.

Spherical, cylindrical, and conical indenters account for periodic boundaries in two ways. First, the center point of a spherical indenter (x,y,z) or axis of a cylindrical/conical indenter (c1,c2) is remapped back into the simulation box, if the box is periodic in a particular dimension. This occurs every timestep if the indenter geometry is specified with a variable (see below), e.g. it is moving over time. Second, the calculation of distance to the indenter center or axis accounts for periodic boundaries. Both of these mean that an indenter can effectively move through and straddle one or more periodic boundaries.

A planar indenter (gstyle = plane) behaves like an axis-aligned infinite-extent wall with the same force expression on atoms in the system as before, but where R is the position of the plane and r-R is the distance of an from the plane. If the side parameter of the plane is specified as lo then it will indent from the lo end of the simulation box, meaning that atoms with a coordinate less than the plane’s current position will be pushed towards the hi end of the box and atoms with a coordinate higher than the plane’s current position will feel no force. Vice versa if side is specified as hi.

Any of the 4 quantities defining a spherical indenter’s geometry can be specified as an equal-style variable, namely x, y, z, or R. For a cylindrical indenter, any of the 3 quantities c1, c2, or R, can be a variable. For a conical indenter, any of the 6 quantities c1, c2, radlo, radhi, lo, or hi can be a variable. For a planar indenter, the single value pos can be a variable.

If any of these values is a variable, it should be specified as v_name, where name is the variable name. In this case, the variable will be evaluated each timestep, and its value used to define the indenter geometry.

Note that equal-style variables can specify formulas with various mathematical functions, and include thermo_style command keywords for the simulation box parameters and timestep and elapsed time. Thus it is easy to specify indenter properties that change as a function of time or span consecutive runs in a continuous fashion. For the latter, see the start and stop keywords of the run command and the elaplong keyword of thermo_style custom for details.

For example, if a spherical indenter’s x-position is specified as v_x, then this variable definition will keep it’s center at a relative position in the simulation box, 1/4 of the way from the left edge to the right edge, even if the box size changes:

variable x equal "xlo + 0.25*lx"

Similarly, either of these variable definitions will move the indenter from an initial position at 2.5 at a constant velocity of 5:

variable x equal "2.5 + 5*elaplong*dt"
variable x equal vdisplace(2.5,5)

If a spherical indenter’s radius is specified as v_r, then these variable definitions will grow the size of the indenter at a specified rate.

variable r0 equal 0.0
variable rate equal 1.0
variable r equal "v_r0 + step*dt*v_rate"

If the side keyword is specified as out, which is the default, then particles outside the indenter are pushed away from its outer surface, as described above. This only applies to spherical, cylindrical, and conical indenters. If the side keyword is specified as in, the action of the indenter is reversed. Particles inside the indenter are pushed away from its inner surface. In other words, the indenter is now a containing wall that traps the particles inside it. If the radius shrinks over time, it will squeeze the particles.

The units keyword determines the meaning of the distance units used to define the indenter geometry. A box value selects standard distance units as defined by the units command, e.g. Angstroms for units = real or metal. A lattice value means the distance units are in lattice spacings. The lattice command must have been previously used to define the lattice spacing. The (x,y,z) coords of the indenter position are scaled by the x,y,z lattice spacings respectively. The radius of a spherical or cylindrical indenter is scaled by the x lattice spacing.

Note that the units keyword only affects indenter geometry parameters specified directly with numbers, not those specified as variables. In the latter case, you should use the xlat, ylat, zlat keywords of the thermo_style command if you want to include lattice spacings in a variable formula.

The force constant K is not affected by the units keyword. It is always in force/distance^2 units where force and distance are defined by the units command. If you wish K to be scaled by the lattice spacing, you can define K with a variable whose formula contains xlat, ylat, zlat keywords of the thermo_style command, e.g.

variable k equal 100.0/xlat/xlat
fix 1 all indent $k sphere ...

Restart, fix_modify, output, run start/stop, minimize info

No information about this fix is written to binary restart files.

The fix_modify energy option is supported by this fix to add the energy of interaction between atoms and the indenter to the global potential energy of the system as part of thermodynamic output. The default setting for this fix is fix_modify energy no. The energy of each particle interacting with the indenter is K/3 (r - R)^3.

The fix_modify respa option is supported by this fix. This allows to set at which level of the r-RESPA integrator the fix is adding its forces. Default is the outermost level.

This fix computes a global scalar energy and a global 3-vector of forces (on the indenter), which can be accessed by various output commands. The scalar and vector values calculated by this fix are “extensive”.

The forces due to this fix are imposed during an energy minimization, invoked by the minimize command. Note that if you define the indenter geometry with a variable using a time-dependent formula, LAMMPS uses the iteration count in the minimizer as the timestep. But it is almost certainly a bad idea to have the indenter change its position or size during a minimization. LAMMPS does not check if you have done this.

Note

If you want the atom/indenter interaction energy to be included in the total potential energy of the system (the quantity being minimized), you must enable the fix_modify energy option for this fix.

Restrictions

none

Related commands

none

Default

The option defaults are side = out and units = lattice.