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.. index:: compute fabric
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compute fabric command
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======================
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Syntax
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""""""
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.. parsed-literal::
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compute ID group-ID fabric cutoff attribute1 attribute2 ... keyword values ...
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* ID, group-ID are documented in :doc:`compute <compute>` command
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* fabric = style name of this compute command
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* cutoff = *type* or *radius*
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.. parsed-literal::
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*type* = cutoffs determined based on atom types
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*radius* = cutoffs determined based on atom diameters (atom style sphere)
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* one or more attributes may be appended
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.. parsed-literal::
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*contact* = contact tensor
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*branch* = branch tensor
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*force/normal* = normal force tensor
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*force/tangential* = tangential force tensor
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* zero or more keyword/value pairs may be appended
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* keyword = *type/include*
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.. parsed-literal::
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*type/include* value = arg1 arg2
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arg = separate lists of types (see below)
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Examples
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""""""""
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.. code-block:: LAMMPS
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compute 1 all fabric type contact force/normal type/include 1,2 3*4
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compute 1 all fabric radius force/normal force/tangential
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Description
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"""""""""""
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Define a compute that calculates various fabric tensors for pairwise
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interaction :ref:`(Ouadfel) <Ouadfel>`. Fabric tensors are commonly used
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to quantify the anisotropy or orientation of granular contacts but can also
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be used to characterize the direction of pairwise interactions in general
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systems. The *type* and *radius* settings are used to select whether interactions
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cutoffs are determined by atom types or by the sum of atomic radii (atom
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style sphere), respectively. Calling this compute is roughly the cost of a
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pair style invocation as it involves a loop over the neighbor list. If the
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normal or tangential force tensors are requested, it will be more expensive
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than a pair style invocation as it will also recalculate all pair forces.
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Four fabric tensors are available: the contact, branch, normal force, or
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tangential force tensor. The contact tensor is calculated as
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.. math::
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C_{ab} = \frac{15}{2} (\phi_{ab} - \mathrm{tr}(\phi) \delta_{ab})
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where :math:`a` and :math:`b` are the :math:`x`, :math:`y`, :math:`z`
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directions, :math:`\delta_{ab}` is the Kronecker delta function, and
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the tensor :math:`\phi` is defined as
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.. math::
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\phi_{ab} = \sum_{n = 1}^{N_p} \frac{r_{a} r_{b}}{r^2}
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where :math:`n` loops over the :math:`N_p` pair interactions in the simulation,
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:math:`r_{a}` is the :math:`a` component of the radial vector between the
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two pairwise interacting particles, and :math:`r` is the magnitude of the radial vector.
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The branch tensor is calculated as
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.. math::
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B_{ab} = \frac{15}{6 \mathrm{tr}(D)} (D_{ab} - \mathrm{tr}(D) \delta_{ab})
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where the tensor :math:`D` is defined as
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.. math::
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D_{ab} = \sum_{n = 1}^{N_p}
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\frac{1}{N_c (r^2 + C_{cd} r_c r_d)}
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\frac{r_{a} r_{b}}{r}
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where :math:`N_c` is the total number of contacts in the system and the subscripts
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:math:`c` and :math:`d` indices are summed according to Einstein notation.
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The normal force fabric tensor is calculated as
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.. math::
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F^n_{ab} = \frac{15}{6 \mathrm{tr}(N)} (N_{ab} - \mathrm{tr}(N) \delta_{ab})
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where the tensor :math:`N` is defined as
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.. math::
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N_{ab} = \sum_{n = 1}^{N_p}
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\frac{1}{N_c (r^2 + C_{cd} r_c r_d)}
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\frac{r_{a} r_{b}}{r^2} f_n
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and :math:`f_n` is the magnitude of the normal, central-body force between the two atoms.
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Finally, the tangential force fabric tensor is only defined for pair styles that
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apply tangential forces to particles, namely granular pair styles. It is calculated
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as
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.. math::
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F^t_{ab} = \frac{15}{9 \mathrm{tr}(N)} (T_{ab} - \mathrm{tr}(T) \delta_{ab})
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where the tensor :math:`T` is defined as
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.. math::
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T_{ab} = \sum_{n = 1}^{N_p}
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\frac{1}{N_c (r^2 + C_{cd} r_c r_d)}
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\frac{r_{a} r_{b}}{r^2} f_t
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and :math:`f_t` is the magnitude of the tangential force between the two atoms.
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The *type/include* keyword filters interactions based on the types of the two atoms.
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Interactions between two atoms are only included in calculations if the atom types
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are in the two lists. Each list consists of a series of type
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ranges separated by commas. The range can be specified as a
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single numeric value, or a wildcard asterisk can be used to specify a range
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of values. This takes the form "\*" or "\*n" or "n\*" or "m\*n". For
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example, if M = the number of atom types, then an asterisk with no numeric
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values means all types from 1 to M. A leading asterisk means all types
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from 1 to n (inclusive). A trailing asterisk means all types from n to M
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(inclusive). A middle asterisk means all types from m to n (inclusive).
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Multiple *type/include* keywords may be added.
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Output info
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"""""""""""
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This compute calculates a local vector of doubles and a scalar. The vector stores the
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unique components of the first requested tensor in the order xx, yy, zz, xy, xz, yz
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followed by the same components for all subsequent tensors. The length of the vector
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is therefore six times the number of requested tensors. The scalar output is the
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number of pairwise interactions included in the calculation of the fabric tensor.
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Restrictions
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""""""""""""
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This fix is part of the GRANULAR package. It is only enabled if LAMMPS
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was built with that package. See the :doc:`Build package <Build_package>`
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doc page for more info.
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Currently, compute *fabric* does not support pair styles
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with many-body interactions. It also does not
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support models with long-range Coulombic or dispersion forces,
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i.e. the kspace_style command in LAMMPS. It also does not support the
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following fixes which add rigid-body constraints: :doc:`fix shake
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<fix_shake>`, :doc:`fix rattle <fix_shake>`, :doc:`fix rigid
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<fix_rigid>`, :doc:`fix rigid/small <fix_rigid>`. It does not support
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granular pair styles that extend beyond the contact of atomic radii
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(e.g. JKR and DMT).
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Related commands
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""""""""""""""""
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none
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Default
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"""""""
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none
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----------
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.. _Ouadfel:
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**(Ouadfel)** Ouadfel and Rothenburg
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"Stress-force-fabric relationship for assemblies of ellipsoids",
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Mechanics of Materials (2001). (`link to paper <https://doi.org/10.1016/S0167-6636(00)00057-0>`_)
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Axel Kohlmeyer