\(\renewcommand{\AA}{\text{Å}}\)

pair_style peri/pmb command

Accelerator Variants: peri/pmb/omp

pair_style peri/lps command

Accelerator Variants: peri/lps/omp

pair_style peri/ves command

pair_style peri/eps command

Syntax

pair_style style

style = peri/pmb or peri/lps or peri/ves or peri/eps

Examples

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

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

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

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

Description

The peridynamic pair styles implement material models that can be used at the mesoscopic and macroscopic scales. See this document for an overview of LAMMPS commands for Peridynamics modeling.

Note

The BPM package provides an alternative implementation of these peridynamics models as bond_style bpm/peri, with the companion contact pair_style bpm/peri. It covers the same PMB, LPS, VES, and EPS material models recast on the BPM framework and is significantly faster than the peri pair styles documented here. See the Peridynamics Howto for a side-by-side comparison, per-model timings, and guidance on choosing between the two implementations.

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) and (Silling 2007). The implementation of Peridynamics in LAMMPS is described in (Parks). Also see the Peridynamics Howto 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 and doc/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 command as in the examples above, or in the data file or restart files read by the read_data or read_restart 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)

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)

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)

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 viscoelastic model responds very similar to a linear elastic model. For details please see the description in “(Mitchell2011)”.

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 “(Mitchell2011a)”.

Changed in version 4Jul2026.

Note

Prior versions of LAMMPS, had an incorrect the plasticity model in style peri/eps relative to the source report (Mitchell2011a). These affected the evolution of the plastic deviatoric extension and caused significant overshooting of the yield surface. These have since been corrected, however, there is still no radial return rule to ensure the plastic deviatoric extension does not leave the yield surface. This may cause some drift off the surface during long simulations. This possibility for future improvement is tracked as issue #5064.

Bond breaking criterion

For all of these styles a peridynamic bond between particles i and j breaks irreversibly once its stretch \(s = (r - r_0)/r_0\) exceeds a critical stretch. Following (Parks) (eq. 9), the critical stretch of a particle is \(s_0 = s_{00} - \alpha\, s_{min}\), where \(s_{min}\) is the minimum (most compressive) stretch over all of the particle’s bonds, and a bond breaks when \(s > \min(s_{0,i}, s_{0,j})\), i.e. symmetrically from the point of view of both particles.

The s00 and \(\alpha\) coefficients may be chosen differently for each pair of atom types. This makes it possible, for example, to assign a smaller s00 to the bonds across an interface between two materials so that a crack preferentially initiates there. The critical stretch is evaluated per bond using that bond’s own s00 and \(\alpha\) together with the geometric \(s_{min}\) of each endpoint.

Changed in version 4Jul2026.

In previous versions the critical stretch was stored as a single per-particle value computed as the maximum of \(s_{00} - \alpha s\) over a particle’s bonds. That is only equivalent to the criterion above when s00 and \(\alpha\) are identical for all type pairs; with type-dependent coefficients a bond would incorrectly inherit the critical stretch of the surrounding bulk bonds and a weakened interface would not fracture. The criterion is now evaluated per bond so that type-dependent s00 and \(\alpha\) behave as intended.

The compute property/atom s0 per-atom property reports this per-particle critical stretch. Earlier versions of this documentation incorrectly described s0 as the maximum stretch of any bond a particle is part of.

Styles with a 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 on the Accelerator packages page. 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 GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page 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 when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

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 shift option.

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

These pair styles write their information to binary restart files, 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 command. They do not support the inner, middle, outer keywords.

Restrictions

All of these styles are part of the PERI package. They are only enabled if LAMMPS was built with that package. See the Build package page for more info.

Default

none

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

(Silling 2000) Silling, J Mech Phys Solids, 48, 175-209 (2000).

(Silling 2007) Silling, Epton, Weckner, Xu, Askari, J Elasticity, 88, 151-184 (2007).

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

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