# gran tangential history model

## Syntax

    tangential history [other model_type/model_name pairs as described here ] keyword values

- zero or more keyword/value pairs may be appended to the end (after all models are specified)

    heating_tangential_history values = 'on' or 'off'
      on = model contributes to surface heating in the frame of surface sphere/heatable
      off = model does not contributes to surface heating

## Description

This granular model is based on the general description of granular force interaction as described in pair gran.

The spring part of the tangential force (F_t = k_t * u_t) is a “history” effect that accounts for the tangential displacement (“tangential overlap”) between the particles for the duration of the time they are in contact. The tangential overlap (u_t) is calculated by integrating the releative tangential velocity at the contact point over time.

If this model is chosen, then this “tangential overlap” spring force is actually calculated / taken into account.

The coefficient of friction cof is the upper limit of the tangential force through the Coulomb criterion Ft_spring = cof*Fn, where Ft_spring and Fn are the tangential spring and total normal force components. Thus in the Hookean case, the tangential force between 2 particles grows according to a tangential spring and dash-pot model until Ft_spring/Fn = cof and is then held at Ft_spring = Fn*cof until the particles lose contact. In the Hertzian case and other non-linear cases, a similar analogy holds, though the spring is no longer linear.

The damping contribution is only added in time-steps where there is no slip, i.e. the Coulomb criterion is not met.

This model contributes to surface heating in the frame of `surface sphere/heatable` if the appropriate flag is activated (only available in the PREMIUM version).

Coarse-graining information:

Using `coarsegraining` in combination with this command might lead to different dynamics or system state and thus to inconsistancies. However, the influence of this model on the global dynamics or system state might be small so in some cases the results may be valid. This has to be reviewed by a specialist on a case-by-case basis.

Note

`Coarsegraining` may or may not be available in LIGGGHTS(R)-PUBLIC.

## Default

heating_tangential_history = ‘off’