PolycrystalHex

The PolycrystalHex object generates a set of points in 2D space such that hexagonal patterns are generated from a resulting Voronoi Tesselation. The number of grains must be chosen such that the $var element = document.getElementById("moose-equation-05de9692-1f7c-4af0-9bc6-216c3a3aac70");katex.render("\\sqrt[dim=2]{n}", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ root is an even integer. Furthermore, a suitable number must be chosen that is supported by the mesh resolution and grain boundary width. At present, the object is supported for generating hexagons in 2D and hexagonal prisms in 3D with the columnar_3D option. It works with periodic boundary conditions. Once the grain structure has been generated, a coloring algorithm is used to assign order parameters to grains so that a reduced number of order parameters may be used. Typical numbers are given here:

Dimension	Recommended OPs
2D	8

See Polycrystal Initial Conditions for more information.

Typical usage in an input file:

[UserObjects]
  [voronoi]
    type = PolycrystalVoronoi
    grain_num = 100 # Number of grains
    rand_seed = 10
    int_width = 7
  []
  [grain_tracker]
    type = GrainTracker
  []
[]

[ICs]
  [PolycrystalICs]
    [PolycrystalColoringIC]
      polycrystal_ic_uo = voronoi
    []
  []
[]

Description and Syntax

PolycrystalHex

Perturbed hexagonal polycrystal

Input Parameters

variableArray of coupled variables
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Array of coupled variables

Required Parameters

boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
coloring_algorithmjpThe grain neighbor graph coloring algorithm to use: "jp" (DEFAULT) Jones and Plassmann, an efficient coloring algorithm, "power" an alternative stochastic algorithm, "greedy", a greedy assignment algorithm with stochastic updates to guarantee a valid coloring, "bt", a back tracking algorithm that produces good distributions but may experience exponential run time in the worst case scenario (works well on medium to large 2D problems)
Default:jp
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:jp, power, greedy, bt
Controllable:No
Description:The grain neighbor graph coloring algorithm to use: "jp" (DEFAULT) Jones and Plassmann, an efficient coloring algorithm, "power" an alternative stochastic algorithm, "greedy", a greedy assignment algorithm with stochastic updates to guarantee a valid coloring, "bt", a back tracking algorithm that produces good distributions but may experience exponential run time in the worst case scenario (works well on medium to large 2D problems)
columnar_3DFalse3D microstructure will be columnar in the z-direction?
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:3D microstructure will be columnar in the z-direction?
compute_halo_mapsFalseInstruct the Postprocessor to communicate proper halo information to all ranks
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Instruct the Postprocessor to communicate proper halo information to all ranks
compute_var_to_feature_mapFalseInstruct the Postprocessor to compute the active vars to features map
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Instruct the Postprocessor to compute the active vars to features map
connecting_thresholdThe threshold for which an existing feature may be extended (defaults to "threshold")
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The threshold for which an existing feature may be extended (defaults to "threshold")
enable_var_coloringFalseInstruct the Postprocessor to populate the variable index map.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Instruct the Postprocessor to populate the variable index map.
execute_onINITIALThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:INITIAL
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
file_nameFile containing grain centroids, if file_name is provided, the centroids from the file will be used.
C++ Type:FileName
Unit:(no unit assumed)
Controllable:No
Description:File containing grain centroids, if file_name is provided, the centroids from the file will be used.
flood_entity_typeELEMENTALDetermines whether the flood algorithm runs on nodes or elements
Default:ELEMENTAL
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:NODAL, ELEMENTAL
Controllable:No
Description:Determines whether the flood algorithm runs on nodes or elements
grain_num0Number of grains being represented by the order parameters
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Number of grains being represented by the order parameters
grain_patch_size10How many nearest grains KDTree should return
Default:10
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:How many nearest grains KDTree should return
int_width0Width of diffuse interfaces
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Width of diffuse interfaces
op_numArray of coupled variables (num_name)
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Array of coupled variables (num_name)
output_adjacency_matrixFalseOutput the Grain Adjacency Matrix used in the coloring algorithms. Additionally, the grain to OP assignments will be printed
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Output the Grain Adjacency Matrix used in the coloring algorithms. Additionally, the grain to OP assignments will be printed
perturbation_percent0The percent to randomly perturb centers of grains relative to the size of the grain
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The percent to randomly perturb centers of grains relative to the size of the grain
point_patch_size1How many nearest points KDTree should return
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:How many nearest points KDTree should return
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
rand_seed0The random seed
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The random seed
secondary_percolation_boundariesPaired boundaries with "primaryary_percolation_boundaries" parameter
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:Paired boundaries with "primaryary_percolation_boundaries" parameter
specified_boundariesAn optional list of boundaries; if supplied, each feature is checked to determine whether it intersects any of the specified boundaries in this list.
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:An optional list of boundaries; if supplied, each feature is checked to determine whether it intersects any of the specified boundaries in this list.
threshold0.5The threshold value for which a new feature may be started
Default:0.5
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The threshold value for which a new feature may be started
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
use_kdtreeFalseWhether or not to use a KD tree to speedup grain search
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not to use a KD tree to speedup grain search
use_less_than_threshold_comparisonTrueControls whether features are defined to be less than or greater than the threshold value.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Controls whether features are defined to be less than or greater than the threshold value.
var_name_baseArray of coupled variables (base_name)
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:Array of coupled variables (base_name)
x_offset0.5Specifies offset of hexagon grid in x-direction
Default:0.5
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Specifies offset of hexagon grid in x-direction

Optional Parameters

allow_duplicate_execution_on_initialTrueIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
condense_map_infoFalseDetermines whether we condense all the node values when in multimap mode (default: false)
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Determines whether we condense all the node values when in multimap mode (default: false)
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:Yes
Description:Set the enabled status of the MooseObject.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
primary_percolation_boundariesA list of boundaries used in conjunction with the corresponding "secondary_percolation_boundaries" parameter for determining if a feature creates a path connecting any pair of boundaries
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:A list of boundaries used in conjunction with the corresponding "secondary_percolation_boundaries" parameter for determining if a feature creates a path connecting any pair of boundaries
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
use_global_numberingTrueDetermine whether or not global numbers are used to label features on multiple maps (default: true)
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Determine whether or not global numbers are used to label features on multiple maps (default: true)
use_single_mapTrueDetermine whether information is tracked per coupled variable or consolidated into one (default: true)
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Determine whether information is tracked per coupled variable or consolidated into one (default: true)

Advanced Parameters

(moose/modules/phase_field/examples/grain_growth/grain_growth_2D_graintracker.i)

# This simulation predicts GB migration of a 2D copper polycrystal with 100 grains represented with 8 order parameters
# Mesh adaptivity and time step adaptivity are used
# An AuxVariable is used to calculate the grain boundary locations
# Postprocessors are used to record time step and the number of grains

[Mesh]
  # Mesh block.  Meshes can be read in or automatically generated
  type = GeneratedMesh
  dim = 2 # Problem dimension
  nx = 44 # Number of elements in the x-direction
  ny = 44 # Number of elements in the y-direction
  xmax = 1000 # maximum x-coordinate of the mesh
  ymax = 1000 # maximum y-coordinate of the mesh
  elem_type = QUAD4 # Type of elements used in the mesh
  uniform_refine = 2 # Initial uniform refinement of the mesh
[]

[GlobalParams]
  # Parameters used by several kernels that are defined globally to simplify input file
  op_num = 8 # Number of order parameters used
  var_name_base = gr # Base name of grains
[]

[Modules]
  [PhaseField]
    [GrainGrowth]
    []
  []
[]

[UserObjects]
  [voronoi]
    type = PolycrystalVoronoi
    grain_num = 100 # Number of grains
    rand_seed = 10
    int_width = 7
  []
  [grain_tracker]
    type = GrainTracker
  []
[]

[ICs]
  [PolycrystalICs]
    [PolycrystalColoringIC]
      polycrystal_ic_uo = voronoi
    []
  []
[]

[AuxVariables]
  # Dependent variables
  [unique_grains]
    order = CONSTANT
    family = MONOMIAL
  []
  [var_indices]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  # AuxKernel block, defining the equations used to calculate the auxvars
  [bnds_aux]
    # AuxKernel that calculates the GB term
    type = BndsCalcAux
    variable = bnds
    execute_on = 'initial timestep_end'
  []
  [unique_grains]
    type = FeatureFloodCountAux
    variable = unique_grains
    flood_counter = grain_tracker
    field_display = UNIQUE_REGION
    execute_on = 'initial timestep_end'
  []
  [var_indices]
    type = FeatureFloodCountAux
    variable = var_indices
    flood_counter = grain_tracker
    field_display = VARIABLE_COLORING
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  # Boundary Condition block
  [Periodic]
    [All]
      auto_direction = 'x y' # Makes problem periodic in the x and y directions
    []
  []
[]

[Materials]
  [CuGrGr]
    # Material properties
    type = GBEvolution
    T = 450 # Constant temperature of the simulation (for mobility calculation)
    wGB = 14 # Width of the diffuse GB
    GBmob0 = 2.5e-6 #m^4(Js) for copper from schonfelder1997molecular bibtex entry
    Q = 0.23 #eV for copper from schonfelder1997molecular bibtex entry
    GBenergy = 0.708 #J/m^2 from schonfelder1997molecular bibtex entry
  []
[]

[Postprocessors]
  # Scalar postprocessors
  [dt]
    # Outputs the current time step
    type = TimestepSize
  []
[]

[Executioner]
  type = Transient # Type of executioner, here it is transient with an adaptive time step
  scheme = bdf2 # Type of time integration (2nd order backward euler), defaults to 1st order backward euler

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  # Uses newton iteration to solve the problem.
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'

  l_max_its = 50 # Max number of linear iterations
  l_tol = 1e-4 # Relative tolerance for linear solves
  nl_max_its = 10 # Max number of nonlinear iterations

  end_time = 4000

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20 # Initial time step.  In this simulation it changes.
    optimal_iterations = 6 # Time step will adapt to maintain this number of nonlinear iterations
  []

  [Adaptivity]
    # Block that turns on mesh adaptivity. Note that mesh will never coarsen beyond initial mesh (before uniform refinement)
    initial_adaptivity = 2 # Number of times mesh is adapted to initial condition
    refine_fraction = 0.8 # Fraction of high error that will be refined
    coarsen_fraction = 0.05 # Fraction of low error that will coarsened
    max_h_level = 2 # Max number of refinements used, starting from initial mesh (before uniform refinement)
  []
[]

[Outputs]
  exodus = true # Exodus file will be outputted
  csv = true
[]