reference the Howto from the rest of the manual. Spelling fixes.

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Axel Kohlmeyer 2022-09-29 07:43:01 -04:00
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@ -16,8 +16,8 @@ model is discretized within LAMMPS as described in the original article
:ref:`(Parks) <Parks2>`. An example problem with comments is also
included.
Quickstart
""""""""""
Quick Start
"""""""""""
The peridynamics styles are included in the optional :ref:`PERI package
<PKG-PERI>`. If your LAMMPS executable does not already include the
@ -54,7 +54,7 @@ Some notes on this input example:
- particles must be created on a :doc:`simple cubic lattice <lattice>`
- using the :doc:`atom style peri <atom_style>` is required
- an :doc:`atom map <atom_modify>` is required for indexing particles
- The :doc:`skin distance <neighbor>` used when computing neighborlists
- The :doc:`skin distance <neighbor>` used when computing neighbor lists
should be defined appropriately for your choice of simulation
parameters. The *skin* should be set to a value such that the
peridynamic horizon plus the skin distance is larger than the maximum
@ -254,11 +254,11 @@ extension :math:`\underline{e}^{\rm d}`.
not change as bonds break. It is computed with respect to the bond
family defined at the reference (initial) configuration.
The nonnegative scalar state :math:`\underline{\omega}` is an *influence
function* :ref:`(Silling 2007) <Silling2007_2>`. For more on influence
functions, see :ref:`(Seleson 2010) <Seleson2010>`. If an influence
function :math:`\underline{\omega}` depends only upon the scalar
:math:`\left\Vert \boldsymbol{\xi} \right\Vert`, (i.e.,
The non-negative scalar state :math:`\underline{\omega}` is an
*influence function* :ref:`(Silling 2007) <Silling2007_2>`. For more on
influence functions, see :ref:`(Seleson 2010) <Seleson2010>`. If an
influence function :math:`\underline{\omega}` depends only upon the
scalar :math:`\left\Vert \boldsymbol{\xi} \right\Vert`, (i.e.,
:math:`\underline{\omega}\left<\boldsymbol{\xi}\right> =
\underline{\omega}\left<\left\Vert \boldsymbol{\xi} \right\Vert\right>`\
), then :math:`\underline{\omega}` is a spherical influence function.
@ -369,7 +369,7 @@ critical stretch defined as
s_0(t,\mathbf{\eta},\mathbf{\xi}) = s_{00} - \alpha s_{\min}(t,\mathbf{\eta},\mathbf{\xi}), \qquad s_{\min}(t) = \min_{\mathbf{\xi}} s(t,\mathbf{\eta},\mathbf{\xi}),
where :math:`s_{00}` and :math:`\alpha` are material-dependant
where :math:`s_{00}` and :math:`\alpha` are material-dependent
constants. The history function :math:`\mu` breaks bonds when the
stretch :math:`s` exceeds the critical stretch :math:`s_0`.
@ -557,7 +557,7 @@ described in the :ref:`Damage section <peridamage>`. Bonds are recorded
as broken in a simulation by removing them from the bond family
:math:`\mathcal{F}_i` (see \eqref{eqn:BondFamily}).
A naiive implementation would have us first loop over all bonds and
A naive implementation would have us first loop over all bonds and
compute :math:`s_{min}` in \eqref{eqn:s0}, then loop over all bonds
again and break bonds with a stretch :math:`s > s0` as in
\eqref{eqn:mu}, and finally loop over all particles and compute forces
@ -761,20 +761,20 @@ Pitfalls
**Parallel Scalability**
LAMMPS operates in parallel in a :doc:`spatial-decomposition mode
<Developer_par_part>`, where each processor owns a spatial subdomain of
<Developer_par_part>`, where each processor owns a spatial sub-domain of
the overall simulation domain and communicates with its neighboring
processors via distributed-memory message passing (MPI) to acquire ghost
atom information to allow forces on the atoms it owns to be
computed. LAMMPS also uses Verlet neighbor lists which are recomputed
every few timesteps as particles move. On these timesteps, particles
also migrate to new processors as needed. LAMMPS decomposes the overall
simulation domain so that spatial subdomains of nearly equal volume are
assigned to each processor. When each subdomain contains nearly the same
number of particles, this results in a reasonable load balance among all
processors. As is more typical with some peridynamic simulations, some
subdomains may contain many particles while other subdomains contain few
particles, resulting in a load imbalance that impacts parallel
scalability.
simulation domain so that spatial sub-domains of nearly equal volume are
assigned to each processor. When each sub-domain contains nearly the
same number of particles, this results in a reasonable load balance
among all processors. As is more typical with some peridynamic
simulations, some sub-domains may contain many particles while other
sub-domains contain few particles, resulting in a load imbalance that
impacts parallel scalability.
**Setting the "skin" distance**
@ -937,7 +937,7 @@ In line 2 we specify that SI units are to be used. We specify the
dimension (3) and boundary conditions ("shrink-wrapped") for the
computational domain in lines 3 and 4. In line 5 we specify that
peridynamic particles are to be used for this simulation. In line 7, we
set the "skin" distance used in building the LAMMPS neighborlist. In
set the "skin" distance used in building the LAMMPS neighbor list. In
line 8 we set the lattice constant (in meters) and in line 10 we define
the spatial region where the target will be placed. In line 12 we
specify a rectangular box enclosing the target region that defines the

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@ -2200,6 +2200,7 @@ Foster (UTSA).
**Supporting info:**
* src/PERI: filenames -> commands
* :doc:`Peridynamics Howto <Howto_peri>`
* `doc/PDF/PDLammps_overview.pdf <PDF/PDLammps_overview.pdf>`_
* `doc/PDF/PDLammps_EPS.pdf <PDF/PDLammps_EPS.pdf>`_
* `doc/PDF/PDLammps_VES.pdf <PDF/PDLammps_VES.pdf>`_

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@ -24,16 +24,17 @@ Description
"""""""""""
Define a computation that calculates the per-atom damage for each atom
in a group. This is a quantity relevant for :doc:`Peridynamics models <pair_peri>`. See `this document <PDF/PDLammps_overview.pdf>`_
for an overview of LAMMPS commands for Peridynamics modeling.
in a group. This is a quantity relevant for :doc:`Peridynamics models
<pair_peri>`. See `this document <PDF/PDLammps_overview.pdf>`_ for an
overview of LAMMPS commands for Peridynamics modeling.
The "damage" of a Peridynamics particles is based on the bond breakage
between the particle and its neighbors. If all the bonds are broken
the particle is considered to be fully damaged.
See the `PDLAMMPS user guide <http://www.sandia.gov/~mlparks/papers/PDLAMMPS.pdf>`_ for a formal
definition of "damage" and more details about Peridynamics as it is
implemented in LAMMPS.
See the :doc:`Peridynamics Howto <Howto_peri>` for a formal definition
of "damage" and more details about Peridynamics as it is implemented in
LAMMPS.
This command can be used with all the Peridynamic pair styles.
@ -53,8 +54,9 @@ The per-atom vector values are unitless numbers (damage) :math:`\ge 0.0`.
Restrictions
""""""""""""
This compute is part of the PERI package. It is only enabled if
LAMMPS was built with that package. See the :doc:`Build package <Build_package>` page for more info.
This compute is part of the PERI package. It is only enabled if LAMMPS
was built with that package. See the :doc:`Build package
<Build_package>` page for more info.
Related commands
""""""""""""""""

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@ -24,7 +24,8 @@ Description
"""""""""""
Define a computation that calculates the per-atom dilatation for each
atom in a group. This is a quantity relevant for :doc:`Peridynamics models <pair_peri>`. See `this document <PDF/PDLammps_overview.pdf>`_
atom in a group. This is a quantity relevant for :doc:`Peridynamics
models <pair_peri>`. See `this document <PDF/PDLammps_overview.pdf>`_
for an overview of LAMMPS commands for Peridynamics modeling.
For small deformation, dilatation of is the measure of the volumetric
@ -32,13 +33,14 @@ strain.
The dilatation :math:`\theta` for each peridynamic particle :math:`i` is
calculated as a sum over its neighbors with unbroken bonds, where the
contribution of the :math:`ij` pair is a function of the change in bond length
(versus the initial length in the reference state), the volume
contribution of the :math:`ij` pair is a function of the change in bond
length (versus the initial length in the reference state), the volume
fraction of the particles and an influence function. See the
`PDLAMMPS user guide <http://www.sandia.gov/~mlparks/papers/PDLAMMPS.pdf>`_ for
a formal definition of dilatation.
:doc:`Peridynamics Howto <Howto_peri>` for a formal definition of
dilatation.
This command can only be used with a subset of the Peridynamic :doc:`pair styles <pair_peri>`: peri/lps, peri/ves and peri/eps.
This command can only be used with a subset of the Peridynamic
:doc:`pair styles <pair_peri>`: *peri/lps*, *peri/ves*, and *peri/eps*.
The dilatation value will be 0.0 for atoms not in the specified
compute group.
@ -56,9 +58,9 @@ The per-atom vector values are unitless numbers :math:`(\theta \ge 0.0)`.
Restrictions
""""""""""""
This compute is part of the PERI package. It is only enabled if
LAMMPS was built with that package. See the
:doc:`Build package <Build_package>` page for more info.
This compute is part of the PERI package. It is only enabled if LAMMPS
was built with that package. See the :doc:`Build package
<Build_package>` page for more info.
Related commands
""""""""""""""""

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@ -51,8 +51,9 @@ Description
"""""""""""
The peridynamic pair styles implement material models that can be used
at the mesoscopic and macroscopic scales. See `this document <PDF/PDLammps_overview.pdf>`_ for an overview of LAMMPS commands
for Peridynamics modeling.
at the mesoscopic and macroscopic scales. See `this document
<PDF/PDLammps_overview.pdf>`_ for an overview of LAMMPS commands for
Peridynamics modeling.
Style *peri/pmb* implements the Peridynamic bond-based prototype
microelastic brittle (PMB) model.
@ -66,26 +67,27 @@ peridynamic viscoelastic solid (VES) model.
Style *peri/eps* implements the Peridynamic state-based elastic-plastic
solid (EPS) model.
The canonical papers on Peridynamics are :ref:`(Silling 2000) <Silling2000>`
and :ref:`(Silling 2007) <Silling2007>`. The implementation of Peridynamics
in LAMMPS is described in :ref:`(Parks) <Parks>`. Also see the `PDLAMMPS user guide <http://www.sandia.gov/~mlparks/papers/PDLAMMPS.pdf>`_ for
more details about its implementation.
The canonical papers on Peridynamics are :ref:`(Silling 2000)
<Silling2000>` and :ref:`(Silling 2007) <Silling2007>`. The
implementation of Peridynamics in LAMMPS is described in :ref:`(Parks)
<Parks>`. Also see the :doc:`Peridynamics Howto <Howto_peri>` for more
details about its implementation.
The peridynamic VES and EPS models in PDLAMMPS were implemented by
R. Rahman and J. T. Foster at University of Texas at San Antonio. The
original VES formulation is described in "(Mitchell2011)" and the
original EPS formulation is in "(Mitchell2011a)". Additional PDF docs
that describe the VES and EPS implementations are include in the
LAMMPS distribution in `doc/PDF/PDLammps_VES.pdf <PDF/PDLammps_VES.pdf>`_ and
that describe the VES and EPS implementations are include in the LAMMPS
distribution in `doc/PDF/PDLammps_VES.pdf <PDF/PDLammps_VES.pdf>`_ and
`doc/PDF/PDLammps_EPS.pdf <PDF/PDLammps_EPS.pdf>`_. For questions
regarding the VES and EPS models in LAMMPS you can contact R. Rahman
(rezwanur.rahman at utsa.edu).
The following coefficients must be defined for each pair of atom types
via the :doc:`pair_coeff <pair_coeff>` command as in the examples above,
or in the data file or restart files read by the
:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
commands, or by mixing as described below.
or in the data file or restart files read by the :doc:`read_data
<read_data>` or :doc:`read_restart <read_restart>` commands, or by
mixing as described below.
For the *peri/pmb* style:
@ -96,8 +98,8 @@ For the *peri/pmb* style:
C is the effectively a spring constant for Peridynamic bonds, the
horizon is a cutoff distance for truncating interactions, and s00 and
:math:`\alpha` are used as a bond breaking criteria. The units of c are such
that c/distance = stiffness/volume\^2, where stiffness is
:math:`\alpha` are used as a bond breaking criteria. The units of c are
such that c/distance = stiffness/volume\^2, where stiffness is
energy/distance\^2 and volume is distance\^3. See the users guide for
more details.
@ -110,8 +112,8 @@ For the *peri/lps* style:
* :math:`\alpha` (unitless)
K is the bulk modulus and G is the shear modulus. The horizon is a
cutoff distance for truncating interactions, and s00 and :math:`\alpha` are
used as a bond breaking criteria. See the users guide for more
cutoff distance for truncating interactions, and s00 and :math:`\alpha`
are used as a bond breaking criteria. See the users guide for more
details.
For the *peri/ves* style:
@ -125,12 +127,12 @@ For the *peri/ves* style:
* m_taubi (unitless)
K is the bulk modulus and G is the shear modulus. The horizon is a
cutoff distance for truncating interactions, and s00 and :math:`\alpha` are
used as a bond breaking criteria. m_lambdai and m_taubi are the
cutoff distance for truncating interactions, and s00 and :math:`\alpha`
are used as a bond breaking criteria. m_lambdai and m_taubi are the
viscoelastic relaxation parameter and time constant,
respectively. m_lambdai varies within zero to one. For very small
values of m_lambdai the viscoelastic model responds very similar to a
linear elastic model. For details please see the description in
respectively. m_lambdai varies within zero to one. For very small values
of m_lambdai the viscoelastic model responds very similar to a linear
elastic model. For details please see the description in
"(Mitchell2011)".
For the *peri/eps* style:
@ -165,8 +167,9 @@ shift option.
The :doc:`pair_modify <pair_modify>` table and tail options are not
relevant for these pair styles.
These pair styles write their information to :doc:`binary restart files <restart>`, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.
These pair styles write their information to :doc:`binary restart files
<restart>`, so pair_style and pair_coeff commands do not need to be
specified in an input script that reads a restart file.
These pair styles can only be used via the *pair* keyword of the
:doc:`run_style respa <run_style>` command. They do not support the
@ -177,8 +180,9 @@ These pair styles can only be used via the *pair* keyword of the
Restrictions
""""""""""""
All of these styles are part of the PERI package. They are only
enabled if LAMMPS was built with that package. See the :doc:`Build package <Build_package>` page for more info.
All of these styles are part of the PERI package. They are only enabled
if LAMMPS was built with that package. See the :doc:`Build package
<Build_package>` page for more info.
Related commands
""""""""""""""""

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@ -747,6 +747,7 @@ dirname
discoverable
discretization
discretized
discretizing
disp
dissipative
Dissipative
@ -915,6 +916,7 @@ emax
Emax
Embt
emi
Emmrich
emol
eN
endian
@ -2125,6 +2127,7 @@ modelled
modelling
Modelling
Modine
moduli
mofff
MOFFF
Mohd
@ -2140,6 +2143,7 @@ Monaghan
Monaghans
monodisperse
monodispersity
monolayer
monopole
monovalent
Montalenti
@ -2415,6 +2419,7 @@ normy
normz
Noskov
noslip
notational
noticable
Nout
noutcol
@ -2775,6 +2780,7 @@ ps
Ps
pscreen
pscrozi
Pseudocode
pseudodynamics
pseudopotential
pSp
@ -3134,6 +3140,7 @@ sectoring
sed
segmental
Seifert
Seleson
sellerio
Sellerio
Semaev
@ -3212,7 +3219,7 @@ slategray
slater
Slepoy
Sliozberg
sLLG
sLL
sllod
sm
smallbig
@ -3623,6 +3630,7 @@ unsmoothed
unsolvated
unsplit
unstrained
unstretched
untar
untilted
Unwin