lammps/doc/pair_peri.txt

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:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

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pair_style peri/pmb command :h3
pair_style peri/pmb/omp command :h3
pair_style peri/lps command :h3
pair_style peri/lps/omp command :h3
pair_style peri/ves command :h3
pair_style peri/eps command :h3

[Syntax:]

pair_style style :pre 

style = {peri/pmb} or {peri/lps} or {peri/ves} or {peri/eps}:ul

[Examples:]

pair_style peri/pmb
pair_coeff * * 1.6863e22 0.0015001 0.0005 0.25 :pre

pair_style peri/lps
pair_coeff * * 14.9e9 14.9e9 0.0015001 0.0005 0.25 :pre

pair_style peri/ves
pair_coeff * * 14.9e9 14.9e9 0.0015001 0.0005 0.25 0.5 0.001 :pre

pair_style peri/eps
pair_coeff * * 14.9e9 14.9e9 0.0015001 0.0005 0.25 118.43 :pre

[Description:]

The peridynamic pair styles implement material models that can be used
at the mescscopic 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.

Style {peri/lps} implements the Peridynamic state-based linear
peridynamic solid (LPS) model.

Style {peri/ves} implements the Peridynamic state-based linear
peridynamic viscoelastic solid (VES) model.

Style {peri/eps} implements the Peridynamic state-based elastic-plastic 
solid (EPS) model.

The canonical papers on Peridynamics are "(Silling 2000)"_#Silling2000
and "(Silling 2007)"_#Silling2007.  The implementation of Peridynamics
in LAMMPS is described in "(Parks)"_#Parks.  Also see the "PDLAMMPS
user guide"_http://www.sandia.gov/~mlparks/papers/PDLAMMPS.pdf 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 distro 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 "pair_coeff"_pair_coeff.html command as in the examples above,
or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html
commands, or by mixing as described below.

For the {peri/pmb} style:

c (energy/distance/volume^2 units)
horizon (distance units)
s00 (unitless)
alpha (unitless) :ul

C is the effectively a spring constant for Peridynamic bonds, the
horizon is a cutoff distance for truncating interactions, and s00 and
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.

For the {peri/lps} style:

K (force/area units)
G (force/area units)
horizon (distance units)
s00 (unitless)
alpha (unitless) :ul

K is the bulk modulus and G is the shear modulus.  The horizon is a
cutoff distance for truncating interactions, and s00 and alpha are
used as a bond breaking criteria. See the users guide for more
details.

For the {peri/ves} style:

K (force/area units)
G (force/area units)
horizon (distance units)
s00 (unitless)
alpha (unitless) 
m_lambdai (unitless)
m_taubi (unitless) :ul

K is the bulk modulus and G is the shear modulus. The horizon is a
cutoff distance for truncating interactions, and s00 and 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 viscoelsatic model responds very similar to a
linear elastic model. For details please see the description in
"(Mtchell2011)".

For the {peri/eps} style:

K (force/area units)
G (force/area units)
horizon (distance units)
s00 (unitless)
alpha (unitless) 
m_yield_stress (force/area units)

K is the bulk modulus and G is the shear modulus. The horizon is a
cutoff distance and s00 and alpha are used as a bond breaking
criteria.  m_yield_stress is the yield stress of the material. For
details please see the description in "(Mtchell2011a)".

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Styles with a {cuda}, {gpu}, {intel}, {kk}, {omp}, or {opt} suffix are
functionally the same as the corresponding style without the suffix.
They have been optimized to run faster, depending on your available
hardware, as discussed in "Section_accelerate"_Section_accelerate.html
of the manual.  The accelerated styles take the same arguments and
should produce the same results, except for round-off and precision
issues.

These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
KOKKOS, USER-OMP and OPT packages, respectively.  They are only
enabled if LAMMPS was built with those packages.  See the "Making
LAMMPS"_Section_start.html#start_3 section for more info.

You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the "-suffix command-line
switch"_Section_start.html#start_7 when you invoke LAMMPS, or you can
use the "suffix"_suffix.html command in your input script.

See "Section_accelerate"_Section_accelerate.html of the manual for
more instructions on how to use the accelerated styles effectively.

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[Mixing, shift, table, tail correction, restart, rRESPA info]:

These pair styles do not support mixing.  Thus, coefficients for all
I,J pairs must be specified explicitly.

These pair styles do not support the "pair_modify"_pair_modify.html
shift option.

The "pair_modify"_pair_modify.html table and tail options are not
relevant for these pair styles.

These pair styles write their information to "binary restart
files"_restart.html, 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
"run_style respa"_run_style.html command.  They do not support the
{inner}, {middle}, {outer} keywords.

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[Restrictions:]

All of these styles are part of the PERI package. They are only
enabled if LAMMPS was built with that package.  See the "Making
LAMMPS"_Section_start.html#start_3 section for more info.

[Related commands:]

"pair_coeff"_pair_coeff.html

[Default:] none

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:link(Parks)
[(Parks)] Parks, Lehoucq, Plimpton, Silling, Comp Phys Comm, 179(11),
777-783 (2008).

:link(Silling2000)
[(Silling 2000)] Silling, J Mech Phys Solids, 48, 175-209 (2000).

:link(Silling2007)
[(Silling 2007)] Silling, Epton, Weckner, Xu, Askari, J Elasticity,
88, 151-184 (2007).

:link(Mitchell2011)
[(Mitchell2011)] Mitchell. A non-local, ordinary-state-based
viscoelasticity model for peridynamics. Sandia National Lab Report,
8064:1-28 (2011).

:link(Mitchell2011a)
[(Mitchell2011a)] Mitchell. A Nonlocal, Ordinary, State-Based
Plasticity Model for Peridynamics. Sandia National Lab Report,
3166:1-34 (2011).