3.16. Granular Sub-Model styles

In granular models, particles are spheres with a finite radius and rotational degrees of freedom as further described in the Howto granular page. Interactions between pair of particles or particles and walls may therefore depend on many different modes of motion as described in pair granular and fix wall/gran. In both cases, the exchange of forces, torques, and heat flow between two types of bodies is defined using a GranularModel class. The GranularModel class organizes the details of an interaction using a series of granular sub-models each of which describe a particular interaction mode (e.g. normal forces or rolling friction). From a parent GranSubMod class, several types of sub-model classes are derived:

  • GranSubModNormal: normal force sub-model

  • GranSubModDamping: normal damping sub-model

  • GranSubModTangential: tangential forces and sliding friction sub-model

  • GranSubModRolling: rolling friction sub-model

  • GranSubModTwisting: twisting friction sub-model

  • GranSubModHeat: heat conduction sub-model

For each type of sub-model, more classes are further derived, each describing a specific implementation. For instance, from the GranSubModNormal class the GranSubModNormalHooke, GranSubModNormalHertz, and GranSubModNormalJKR classes are derived which calculate Hookean, Hertzian, or JKR normal forces, respectively. This modular structure simplifies the addition of new granular contact models as one only needs to create a new GranSubMod class without having to modify the more complex PairGranular, FixGranWall, and GranularModel classes. Most GranSubMod methods are also already defined by the parent classes so new contact models typically only require edits to a few relevant methods (e.g. methods that define coefficients and calculate forces).

Each GranSubMod class has a pointer to both the LAMMPS class and the GranularModel class which owns it, lmp and gm, respectively. The GranularModel class includes several public variables that describe the geometry/dynamics of the contact such as

xi and xj

Positions of the two contacting bodies

vi and vj

Velocities of the two contacting bodies

omegai and omegaj

Angular velocities of the two contacting bodies

dx and nx

The displacement and normalized displacement vectors

r, rsq, and rinv

The distance, distance squared, and inverse distance


The sum of particle radii

vr, vn, and vt

The relative velocity vector and its normal and tangential components


The relative rotational velocity

These quantities, among others, are calculated in the GranularModel->check_contact() and GranularModel->calculate_forces() methods which can be referred to for more details.

To create a new GranSubMod class, it is recommended that one first looks at similar GranSubMod classes. All GranSubMod classes share several general methods which may need to be defined


Optional method to define how coefficients are mixed for different atom types. By default, coefficients are mixed using a geometric mean.


Parses coefficients to define local variables. Run once at model construction.


Optional method to define local variables after other GranSubMod types were created. For instance, this method may be used by a tangential model that derives parameters from the normal model.

There are also several type-specific methods


Optional method to test when particles are in contact. By default, this is when particles overlap.


Optional method to return the distance at which particles stop interacting. By default, this is when particles no longer overlap.


Optional method to return the radius of the contact. By default, this returns the radius of the geometric cross section.


Optional method that defines the critical force to break the contact used by some tangential, rolling, and twisting sub-models. By default, this is the current total normal force including damping.


Required method that returns the normal contact force


Required method that returns the normal damping force


Required method that calculates tangential forces/torques


Required method that calculates twisting friction forces/torques


Required method that calculates rolling friction forces/torques


Required method that returns the rate of heat flow

As an example, say one wanted to create a new normal force option that consisted of a Hookean force with a piecewise stiffness. This could be done by adding a new set of files gran_sub_mod_custom.h:

#ifdef GranSubMod_CLASS
// clang-format off
// clang-format on


#include "gran_sub_mod.h"
#include "gran_sub_mod_normal.h"

namespace LAMMPS_NS {
namespace Granular_NS {
  class GranSubModNormalHookePiecewise : public GranSubModNormal {
    GranSubModNormalHookePiecewise(class GranularModel *, class LAMMPS *);
    void coeffs_to_local() override;
    double calculate_forces() override;
    double k1, k2, delta_switch;

}    // namespace Granular_NS
}    // namespace LAMMPS_NS

#endif /*GRAN_SUB_MOD_CUSTOM_H_ */
#endif /*GRAN_SUB_MOD_CLASS_H_ */

and gran_sub_mod_custom.cpp

#include "gran_sub_mod_custom.h"
#include "gran_sub_mod_normal.h"
#include "granular_model.h"

using namespace LAMMPS_NS;
using namespace Granular_NS;

GranSubModNormalHookePiecewise::GranSubModNormalHookePiecewise(GranularModel *gm, LAMMPS *lmp) :
    GranSubModNormal(gm, lmp)
  num_coeffs = 4;

/* ---------------------------------------------------------------------- */

void GranSubModNormalHookePiecewise::coeffs_to_local()
  k1 = coeffs[0];
  k2 = coeffs[1];
  damp = coeffs[2];
  delta_switch = coeffs[3];

/* ---------------------------------------------------------------------- */

double GranSubModNormalHookePiecewise::calculate_forces()
  double Fne;
  if (gm->delta >= delta_switch) {
    Fne = k1 * delta_switch + k2 * (gm->delta - delta_switch);
  } else {
    Fne = k1 * gm->delta;
  return Fne;