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### fix wall/gran command

Syntax:

    fix ID group-ID wall/gran Kn Kt gamma_n gamma_t xmu dampflag style args ... keyword values ...

- ID, group-ID are documented in fix command
- wall/gran = style name of this fix command
- Kn = elastic constant for normal particle repulsion (force/distance units or pressure units - see discussion below)
- Kt = elastic constant for tangential contact (force/distance units or pressure units - see discussion below)
- gamma_n = damping coefficient for collisions in normal direction (1/time units or 1/time-distance units - see discussion below)
- gamma_t = damping coefficient for collisions in tangential direction (1/time units or 1/time-distance units - see discussion below)
- xmu = static yield criterion (unitless fraction between 0.0 and 1.0)
- dampflag = 0 or 1 if tangential damping force is excluded or included
- one or more style/arg pairs may be appended
- style = xlo or xhi or ylo or yhi or zlo or zhi or zcylinder
- args = list of arguments for a particular style

        xlo or xhi or ylo or yhi or zlo or zhi args = coord vwall
          coord = position of wall = constant or variable
            constant = number like 0.0 or -30.0 (distance units)
            variable = equal-style variable like v_x or v_wiggle
          vwall = velocity of wall in normal direction = constant or variable
            constant = number like 0.0 or 2.0 (velocity units)
            variable = equal-style variable like v_vx or v_wiggle
        zcylinder args = rad vrad
          rad = radius of cylinder = constant or variable
            constant = number like 0.0 or -30.0 (distance units)
            variable = equal-style variable like v_rad or v_wiggle
          vwall = velocity of radius in normal direction = constant or variable
            constant = number like 0.0 or 2.0 (velocity units)
            variable = equal-style variable like v_vrad or v_wiggle

- zero or more keyword/value pairs may be appended to args
- keyword = shear or piston

        shear values = dim vshear
          dim = x or y or z or theta
          vshear = shear velocity = constant or variable
            constant = number like 2.0 or -2.0 (velocity units or radians/time units)
            variable = equal-style variable like v_vshear or v_wiggle
        piston values = pload pmass
          pload = external load on piston = constant or variable
            constant = number like 0.0 or 30.0 (force units)
            variable = equal-style variable like v_push or v_wiggle
          pmass = piston mass (mass units)

Examples:

    fix 1 all wall/gran 200000.0 NULL 50.0 NULL 0.5 0 xlo -10.0 0 xhi 10.0 0
    fix 1 all wall/gran 200000.0 NULL 50.0 NULL 0.5 0 zhi v_squeeze shear x v_ramp
    fix 2 all wall/gran 100000.0 20000.0 50.0 30.0 0.5 1 zcylinder 15.0 0.0 piston -5000.0 1000.0

Description:

Bound the simulation domain of a granular system with one or more frictional walls. All particles in the group interact with the wall when they are close enough to touch it.

The first set of parameters (Kn, Kt, gamma_n, gamma_t, xmu, and dampflag) have the same meaning as those specified with the pair_style granular force fields. This means a NULL can be used for either Kt or gamma_t as described on that page. If a NULL is used for Kt, then a default value is used where Kt = 2/7 Kn. If a NULL is used for gamma_t, then a default value is used where gamma_t = 1/2 gamma_n.

The nature of the wall/particle interactions are determined by which pair_style is used in your input script: hooke, hooke/history, or hertz/history. The equation for the force between the wall and particles touching it is the same as the corresponding equation on the pair_style granular doc page, in the limit of one of the two particles going to infinite radius and mass (flat wall). I.e. delta = radius - r = overlap of particle with wall, m_eff = mass of particle, and sqrt(RiRj/Ri+Rj) becomes sqrt(radius of particle). The units for Kn, Kt, gamma_n, and gamma_t are as described on that doc page. The meaning of xmu and dampflag are also as described on that page. Note that you can choose different values for these 6 wall/particle coefficients than for particle/particle interactions, if you wish your wall to interact differently with the particles, e.g. if the wall is a different material.

IMPORTANT NOTE: As discussed on the doc page for pair_style granular, versions of LAMMPS before 9Jan09 used a different equation for Hertzian interactions. This means Hertizian wall/particle interactions have also changed. They now include a sqrt(radius) term which was not present before. Also the previous versions used Kn and Kt from the pairwise interaction and hardwired dampflag to 1, rather than letting them be specified directly. This means you can set the values of the wall/particle coefficients appropriately in the current code to reproduce the results of a prevoius Hertzian monodisperse calculation. For example, for the common case of a monodisperse system with particles of diameter 1, Kn, Kt, gamma_n, and gamma_s should be set sqrt(2.0) larger than they were previously.

One or more wall styles can be specified. The xlo, xhi, ylo, yhi, zlo, zhi styles are planar faces that push particles back into the box from one of their sides. E.g. the xlo wall should be positioned to the left of all particles in the x dimension, so that it pushes particles to the right, and conversely for the xhi wall. The zcylinder style is a cylindrical shell with its axis along the z-axis, centered at x = y = 0.0. The interior surface of the cylinder pushes particles towards the x = y = 0.0 center axis. The zcylinder style cannot be specified with any of the xlo, xhi, ylo, yhi styles, but if can be with the zlo or zhi styles.

For the planer wall styles, coord and vwall arguments are specified. These are the position and normal velocity of the wall. A positive velocity means the wall is moving in the positive direction in the normal dimension, e.g. +x for a xlo or xhi wall. Either or both of the coord and vwall arguments can be specified as a constant value or a variable. Note that the force exerted by a wall on granular particles depends on the velocity of the wall, in both the normal and tangential directions, so it is important to set vwall consistent with the coord argument.

If a numeric constant is specified for coord then the wall is placed at that position in the appropriate dimension (x, y, or z) and will never move. Likewise if a constant is specified for vwall, then the normal velocity of the wall is set to that value and will never change.

If coord or vwall is a variable, it should be specified as v_name, where name is an equal-style variable name. In this case the variable is evaluated each timestep and the result becomes the current position or normal velocity of the wall. 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 a time-dependent wall position and velocity.

If coord is specified as a constant, then vwall must be specified as 0.0. If coord is specified as a variable, then vwall must be a non-zero constant or a variable. If vwall is specified as a non-zero constant or variable and coord as a constant, then coord is treated as the initial position of the wall, and the wall position is updated each timestep by dt*v_current, where dt = the timestep, and v_current = the current normal velocity.

For the zcylinder wall style, rad and vrad arguments are specified. These are the radius and radial velocity of the cylinder. A positive velocity means the radius is growing. Either or both of the rad and vrad arguments can be specified as a constant value or a variable. Note that the force exerted by the wall of the cylinder on granular particles depends on the velocity of the wall, in both the normal (radial) and tangential directions, so it is important to set vrad consistent with the rad argument.

If a numeric constant is specified for rad then the cylinder will have a fixed radius. Likewise if a constant is specified for vrad, then the radial velocity of the cylinder is set to that value and will never change.

If rad or vrad is a variable, it should be specified as v_name, where name is an equal-style variable name. In this case the variable is evaluated each timestep and the result becomes the current radius or radial velocity of the cylinder. 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 a time-dependent cylinder radius and velocity.

If rad is specified as a constant, then vrad must be specified as 0.0. If rad is specified as a variable, then vrad must be a non-zero constant or a variable. If vrad is specified as a non-zero constant or variable and rad as a constant, then rad is treated as the initial radius of the wall, and the radius is updated each timestep by dt*v_current, where dt = the timestep, and v_current = the current radial velocity.

Here are examples of variable definitions that move the wall position in a time-dependent fashion using equal-style variables. They also specify the correct normal velocity of the wall based on the time derivative of the position.

    variable ramp equal ramp(0,10)
    variable vnorm equal 10/(10000*dt)  # 10000 step run
    fix 1 all wall/gran ... xlo v_ramp v_vnorm

    variable linear equal vdisplace(0,20)
    fix 1 all wall/gran ... xlo v_linear 20

    variable omega equal 2*PI/3.0
    variable wiggle equal swiggle(0.0,5.0,3.0)
    variable vwiggle equal "5.0 * v_omega * cos(v_omega*(timestep-startstep)*dt)"
    fix 1 all wall/gran ... xlo v_wiggle v_vwiggle

    variable omega equal 2*PI/3.0
    variable wiggle equal cwiggle(0.0,5.0,3.0)
    variable vwiggle equal "5.0 * v_omega * sin(v_omega*(timestep-startstep)*dt)"
    fix 1 all wall/gran ... xlo v_wiggle v_vwiggle

The ramp(lo,hi) function adjusts the wall position linearly from lo to hi over the course of a run. The vdisplace(c0,velocity) function does something similar using the equation position = c0 + velocity*delta, where delta is the elapsed time.

The swiggle(c0,A,period) function causes the wall position to oscillate sinusoidally according to this equation, where omega = 2 PI / period:

    position = c0 + A sin(omega*delta)

The cwiggle(c0,A,period) function causes the wall position to oscillate sinusoidally according to this equation, which will have an initial wall velocity of 0.0, and thus may impose a gentler perturbation on the particles:

    position = c0 + A (1 - cos(omega*delta))

The optional keywords shear and piston are applied to all the specified wall styles. If you need to apply different options to different wall styles, then you should use multiple fix wall/gran commands.

The shear keyword allows specification of one or two tangential velocities for planar or zcylinder walls. The dim value specifies the velocity direction. X, y, and z can be used for planar walls, but not for the direction normal to the wall. Z and theta can be used for a zcylinder wall. Theta is the azimuthal angle in the xy plane, i.e. a rotation of the cylinder about its vertical z axis. Note that a positive theta velocity means increasing theta, i.e. rotation in a counter-clockwise direction when looking down on the xy plane from above.

Vshear is the magnitude of the shear velocity and can be specified as a numeric constant or variable. The units of vshear are velocity units for dim = x, y, or z. They are units of radians/time for dim = theta.

If a numeric constant is used, then then the shear velocity will never change. If vshear is a variable, it should be specified as v_name, where name is an equal-style variable name. In this case the variable is evaluated each timestep and the result becomes the current shear velocity. 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 a time-dependent shear velocity.

The piston keyword allows specification of an external loading force on the wall, which is opposed by granular particles pushing back against the load. The wall position and normal velocity adjust dynamically in response to these 2 opposing forces.

Pload is the magnitude of the loading force and can be specified as a numeric constant or variable. This force must have a value less than 0.0 which means that it is directed inward towards the particles. Thus for a xlo wall, a negative values is a force in the +x direction. For a xhi wall a negative values is a force in the -x direction. For a zcylinder wall, a negative value is a force towards the center z axis of the cylinder.

If a numeric constant is used for pload, then then the load force will never change. If pload is a variable, it should be specified as v_name, where name is an equal-style variable name. In this case the variable is evaluated each timestep and the result becomes the current load force. 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 a time-dependent load force.

When the piston keyword is used, the coord and vwall arguemnts for each wall style (or rad and vrad arguments for a zcylinder style) must be numeric constants and are treated as initial values of the position/radius and velocity/radial-velocity. The initial values are updated every timestep by integrating these equations in a velocity-Verlet fashion:

    vwall_new = vwall + dt * (Fload + Fparticles) / pmass
    xwall_new = xwall + dt * vwall_new

Fload and Fparticles are the force on the wall due to the external load and interactions with particles respectively. Fparticles is always a positive value, representing particles pushing outward on the wall (-x direction for a xlo wall, +x direction for a xhi wall, radially outward for a zylinder wall). Thus Fload and Fparticles will always have opposite signs. Pmass is the mass of the wall, as specified with the piston keyword. Xwall and Vwall are the wall position (or radius) and normal velocity (or radial velocity) on the previous timestep. Xwall_new and vwall_new are the updated values.

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

This fix writes the shear friction state of atoms interacting with the wall to binary restart files, so that a simulation can continue correctly if granular potentials with shear "history" effects are being used. See the read_restart command for info on how to re-specify a fix in an input script that reads a restart file, so that the operation of the fix continues in an uninterrupted fashion.

The fix does not write any information about the walls (e,g, position or velocity) to the restart file. It is up to you to insure that fix wall/gran commands you re-specify in a restart input script are consistent with the previous simulation.

None of the fix_modify options are relevant to this fix.

This fix computes a global vector of values, which can be accessed by various output commands. The length of the vector is 4*Nstyle, where Nstyle is the number of styles specified.

The 4 values (per style) are as follows:

    (1) position (or radius) of wall (distance units)
    (2) normal (or radial) velocity of wall (velocity or radians/time units)
    (3) positive force on wall due to particles (force units)
    (4) negative force on wall due to external load (force units)

The sign conventions for these values are as described above. The 4th value will be 0.0 if the piston keyword is not used. The vector values calculated by this fix are "extensive".

No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.

Restrictions:

This fix is part of the GRANULAR package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.

Any dimension (xyz) that has a granular wall must be non-periodic.

Related commands:

fix_move, pair_style granular

Default:

The default shear velocities are 0.0.