pair_style smd/tlsph command

Syntax

pair_style smd/tlsph keyword value

zero or one keyword/value pair may be appended

keyword = *UPDATE_CONSTANT or *UPDATE_PAIRWISE

*UPDATE_CONSTANT value = dmax
  dmax = update the reference configuration when the change of a pair distance exceeds dmax (distance units)
*UPDATE_PAIRWISE value = ratio
  ratio = update the reference configuration when the change of a pair distance divided by the kernel range exceeds ratio (unitless)

pair_coeff I I *COMMON rho0 E nu Q1 Q2 hg Cp keyword args ... *END

I = atom type (both types must be the same)
rho0 = reference mass density (mass/volume units)
E = Young’s modulus (pressure units)
nu = Poisson ratio (unitless)
Q1 = linear artificial viscosity coefficient (unitless)
Q2 = quadratic artificial viscosity coefficient (unitless)
hg = hourglass control coefficient (unitless)
Cp = ignored, but must be present
zero or more keyword/args groups may be appended, with at most one equation of state and one strength model

keyword = *EOS_NONE or *EOS_LINEAR or *EOS_SHOCK or *EOS_POLYNOMIAL or *STRENGTH_LINEAR or *STRENGTH_LINEAR_PLASTIC or *JOHNSON_COOK or *FAILURE_MAX_PLASTIC_STRAIN or *FAILURE_MAX_PAIRWISE_STRAIN or *FAILURE_ENERGY_RELEASE_RATE

*EOS_NONE args = none
*EOS_LINEAR args = none
*EOS_SHOCK args = c0 S Gamma
  c0 = reference speed of sound (velocity units)
  S = slope of the linear relation between shock and particle velocity (unitless)
  Gamma = Grueneisen parameter (unitless)
*EOS_POLYNOMIAL args = C0 C1 C2 C3 C4 C5 C6
  C0, C1, C2, C3 = polynomial coefficients (pressure units)
  C4, C5, C6 = ignored, but must be present
*STRENGTH_LINEAR args = none
*STRENGTH_LINEAR_PLASTIC args = sigma_y H
  sigma_y = initial yield stress (pressure units)
  H = hardening parameter (pressure units)
*JOHNSON_COOK args = A B a C epdot0 T0 Tmelt m
  A = initial yield stress (pressure units)
  B = strain hardening factor (pressure units)
  a = strain hardening exponent (unitless)
  C = strain rate factor (unitless)
  epdot0 = reference plastic strain rate (1/time units)
  T0, Tmelt, m = ignored, but must be present
*FAILURE_MAX_PLASTIC_STRAIN args = epsmax
  epsmax = equivalent plastic strain at which a particle fails (unitless)
*FAILURE_MAX_PAIRWISE_STRAIN args = epsmax
  epsmax = pairwise strain at which the degradation of a pair interaction starts (unitless)
*FAILURE_ENERGY_RELEASE_RATE args = Gc
  Gc = critical energy release rate (energy/area units)

*END = keyword that terminates the list of parameters

Examples

pair_style smd/tlsph
pair_coeff 1 1 *COMMON 1.0 1.0 0.3 0.06 0.0 10.0 1.0 &
           *STRENGTH_LINEAR &
           *EOS_LINEAR &
           *END

pair_style smd/tlsph
pair_coeff 1 1 *COMMON 1.0 70.0 0.3 0.56 0.0 10.0 1.0 &
           *EOS_POLYNOMIAL 0.0 74.2 60.5 36.5 1.96 0.0 0.0 &
           *JOHNSON_COOK 0.3241 0.1138 0.42 0.0 1.0e-3 298.15 500.15 1.34 &
           *FAILURE_MAX_PLASTIC_STRAIN 1.2 &
           *END

pair_style hybrid/overlay smd/tlsph smd/hertz 1.0
pair_coeff 1 1 smd/tlsph *COMMON 1.0 1.0 0.3 0.06 0.0 10.0 1.0 &
           *STRENGTH_LINEAR_PLASTIC 0.051 0.0 &
           *EOS_LINEAR &
           *END

Description

The smd/tlsph style computes particle interactions according to continuum mechanics constitutive laws and a total Lagrangian smoothed particle hydrodynamics (TLSPH) algorithm. In this formulation, all SPH expressions are evaluated in the undeformed reference configuration of the material, which avoids the tensile instability of SPH. It is best suited for solids. The method, including the hourglass control and the material models, is explained on the Howto machdyn page.

By default, the reference configuration is the initial configuration and is never changed. With the *UPDATE_CONSTANT or *UPDATE_PAIRWISE keyword, the reference configuration is updated to the current configuration whenever the change of the distance of any pair of interacting particles relative to their reference distance exceeds dmax, or exceeds the fraction ratio of the kernel range, respectively. This is needed when the neighbor relations of the particles change, e.g. due to plastic flow. Please see the Howto machdyn page for what happens during an update. A warning is printed if dmax exceeds the communication cutoff.

In contrast to most other pair styles, the parameters of the pair_coeff command are organized in groups that start with a keyword. The *COMMON keyword with its 7 parameters is mandatory and must come first. From Young’s modulus and the Poisson ratio, the shear modulus, the bulk modulus, and the speed of sound of the material are derived, which are also used by the equations of state and strength models. The *COMMON group can be followed by keywords for an equation of state, which determines the pressure, a strength model, which determines the deviatoric (shear) stress, and failure models. The list of parameters must be terminated with the *END keyword. Using the line continuation operator “&” to put each keyword group on its own line is recommended. If no equation of state or no strength model is given, the pressure or the deviatoric stress is zero, respectively. The available models and their equations are described in the material models section of the Howto machdyn page.

Recommended values for Q1 are between 0.05 and 1.0 and for hg between about 1 and 20.

Only interactions between particles of the same type can be defined, i.e. I and J must be the same. Particles of different types or different bodies can interact through contact forces computed with the smd/hertz pair style, which can be combined with this pair style through pair_style hybrid/overlay.

Mixing, shift, table, tail correction, restart, rRESPA info

No mixing is performed automatically. Currently, no part of MACHDYN supports restarting nor minimization. rRESPA does not apply to this pair style.

Restrictions

This pair style is part of the MACHDYN package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

This pair style requires the atom style smd, an atom map (see the atom_modify command), and the newton setting off. All particles interacting with this pair style must be members of a group named tlsph, and they must be integrated with fix smd/integrate_tlsph.

The *FAILURE_MAX_PAIRWISE_STRAIN keyword cannot be combined with the *UPDATE_CONSTANT or *UPDATE_PAIRWISE keywords.

Default

The reference configuration is not updated.