pair_style smd/ulsph command

Syntax

pair_style smd/ulsph density gradient correction

  • density = *DENSITY_SUMMATION or *DENSITY_CONTINUITY

  • gradient = *VELOCITY_GRADIENT or *NO_VELOCITY_GRADIENT

  • correction = *GRADIENT_CORRECTION or *NO_GRADIENT_CORRECTION

pair_coeff I I *COMMON rho0 c0 Q1 Cp hg keyword args ... *END
pair_coeff I J *CROSS

  • I, J = atom types

  • rho0 = reference mass density (mass/volume units)

  • c0 = reference speed of sound (velocity units)

  • Q1 = linear artificial viscosity coefficient (unitless)

  • Cp = ignored, but must be present

  • hg = hourglass control coefficient (unitless)

  • one or more keyword/args groups must be appended, with exactly one equation of state and at most one strength or viscosity model

  • keyword = *EOS_LINEAR or *EOS_TAIT or *EOS_PERFECT_GAS or *STRENGTH_LINEAR or *STRENGTH_LINEAR_PLASTIC or *VISCOSITY_NEWTON or *ARTIFICIAL_PRESSURE or *ARTIFICIAL_STRESS

    *EOS_LINEAR args = none
*EOS_TAIT args = n
  n = Tait exponent (unitless)
*EOS_PERFECT_GAS args = gamma
  gamma = heat capacity ratio (unitless)
*STRENGTH_LINEAR args = G
  G = shear modulus (pressure units)
*STRENGTH_LINEAR_PLASTIC args = G sigma_y H
  G = shear modulus (pressure units)
  sigma_y = initial yield stress (pressure units)
  H = hardening parameter (pressure units)
*VISCOSITY_NEWTON args = mu
  mu = dynamic viscosity (mass/(distance time) units)
*ARTIFICIAL_PRESSURE args = amplitude
  amplitude = strength of the artificial pressure (unitless)
*ARTIFICIAL_STRESS args = amplitude
  amplitude = strength of the artificial stress (unitless)

  • *END = keyword that terminates the list of parameters

Examples

pair_style smd/ulsph *DENSITY_CONTINUITY *VELOCITY_GRADIENT *NO_GRADIENT_CORRECTION
pair_coeff 1 1 *COMMON 1000.0 10.0 1.0 1.0 0.0 &
           *EOS_TAIT 7.0 &
           *END

pair_style smd/ulsph *DENSITY_CONTINUITY *VELOCITY_GRADIENT *NO_GRADIENT_CORRECTION
pair_coeff 1 1 *COMMON 1000.0 10.0 1.0 1.0 0.0 &
           *EOS_TAIT 7.0 &
           *END
pair_coeff 2 2 *COMMON 1000.0 10.0 1.0 1.0 0.0 &
           *EOS_TAIT 7.0 &
           *VISCOSITY_NEWTON 0.1 &
           *END
pair_coeff 1 2 *CROSS

Description

The smd/ulsph style computes particle interactions according to continuum mechanics constitutive laws and an updated Lagrangian smoothed particle hydrodynamics (ULSPH) algorithm. In this formulation, all SPH expressions are evaluated in the current configuration, so that the particles interacting with a given particle change during a simulation. It is best suited for fluids and for solids undergoing arbitrarily large deformations. The method and the material models are explained on the Howto machdyn page.

The three arguments of the pair style select how the mass density is computed, whether the velocity gradient is computed, and whether the kernel gradients are corrected to first order:

  • *DENSITY_SUMMATION recomputes the mass density every time step by kernel summation, while *DENSITY_CONTINUITY integrates the mass density in time from the rate of deformation.

  • *VELOCITY_GRADIENT enables the computation of the velocity gradient. This is required for *DENSITY_CONTINUITY and for strength and viscosity models. *NO_VELOCITY_GRADIENT saves computation time and is only useful for inviscid fluids.

  • *GRADIENT_CORRECTION computes first-order corrected kernel gradients. This makes the method more accurate, but can lead to severe numerical instabilities if the neighborhood of a particle is ill-defined. For a general fluid simulation, *NO_GRADIENT_CORRECTION is recommended.

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 5 parameters is mandatory and must come first. The bulk modulus of the material is derived from the reference density and speed of sound as \(K = c_0^2 \rho_0\). The *COMMON group must be followed by an equation of state, which determines the pressure, and optionally by either a strength model or a viscosity model, which determine the deviatoric (shear) stress. 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. The available models and their equations are described in the material models section of the Howto machdyn page.

The *ARTIFICIAL_PRESSURE and *ARTIFICIAL_STRESS keywords add Monaghan’s artificial pressure or artificial stress terms, which counteract the clumping of particles under tension (tensile instability).

Interactions between particles of different types I and J, e.g. between a highly viscous and a low viscosity fluid, must be requested with the *CROSS keyword, after the parameters for both types I and J have been set. The amplitudes of the artificial pressure and artificial stress for the cross interaction are the averages of the values for the two types, if both are larger than zero.

Recommended values for Q1 are between 0.05 and 1.0. The hourglass control coefficient hg is usually set to 0 for fluids.

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, and the particles interacting with it must be integrated with fix smd/integrate_ulsph.

A strength model and a viscosity model cannot be used for the same particle type.

Default

none