FFTElasticChemicalPotential

FFT based elastic strain energy chemical potential solve.

Overview

Computes the elastic contribution to the chemical potential in Fourier space for an eigenstrain problem. Given Lam\'e parameters mu and lambda, an eigenstrain amplitude e0, the Fourier transform of a scalar field cbar, and the displacement fields u = (u_x,u_y,u_z), the output is

$var element = document.getElementById("moose-equation-cfa3dd93-d14b-4ebb-a2ef-f6f5e794bf96");katex.render("\\mu_\\text{mech} = -e0 * ( e0 * (9 lambda cbar + 6 mu cbar) - (2 mu + 3 lambda) * div(u) ),", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-5df10f14-6ac2-4108-b5f2-beaacaf715ae");katex.render("\\nabla\\cdot u", element, {displayMode:false,throwOnError:false});$ is evaluated spectrally as $var element = document.getElementById("moose-equation-6014fd6b-757d-4cc3-a260-e12b5f220773");katex.render("i 2 \\pi (k_x \\hat u_x + k_y \\hat u_y + k_z \\hat u_z)", element, {displayMode:false,throwOnError:false});$ .

The resulting tensor is inverse-transformed by downstream operators as needed.

Example Input File Syntax

[TensorComputes]
  [Solve]
    [elastic_mu]
      type = FFTElasticChemicalPotential
      buffer = mubar_elastic
      displacements = 'ux uy uz'
      cbar = cbar
      mu = 1.0
      lambda = 2.0
      e0 = 1e-3
    []
  []
[]
!listing-end

Input Parameters

bufferThe buffer this compute is writing to
C++ Type:std::string
Controllable:No
Description:The buffer this compute is writing to
e0volumetric eigenstrain
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:volumetric eigenstrain
lambdaLame lambda
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Lame lambda
muLame mu
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Lame mu

Required Parameters

cbarFFT of concentration buffer
C++ Type:std::string
Controllable:No
Description:FFT of concentration buffer
displacementsDisplacements
C++ Type:std::vector<std::string>
Controllable:No
Description:Displacements

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/tensor_compute/coupled_pf_mech_secant.i)
(test/tests/tensor_compute/coupled_pf_mech.i)
(test/tests/tensor_compute/group.i)

(test/tests/tensor_compute/coupled_pf_mech_secant.i)

[Domain]
  dim = 3
  nx = 128
  ny = 128
  nz = 128
  xmax = ${fparse pi*4}
  ymax = ${fparse pi*4}
  zmax = ${fparse pi*4}
  mesh_mode = DUMMY
[]

[TensorBuffers]
  # phase field
  [c]
  []
  [cbar]
  []
  [mu]
  []
  [mubar]
  []
  [Mbarmubar]
  []

  # mechanics
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [mumechbar]
  []
  [mumech]
  []

  # constant tensors
  [Mbar]
  []
  [kappabarbar]
  []
[]

[TensorOutputs]
  [xdmf]
    type = XDMFTensorOutput
    buffer = 'c disp_x disp_y disp_z mu mumech'
    output_mode = 'Node Node Node Node Cell Cell'
    enable_hdf5 = true
  []
[]

[TensorComputes]
  [Initialize]
    [c]
      type = RandomTensor
      buffer = c
      min = 0.44
      max = 0.56
    []
    [mu_init]
      type = ConstantTensor
      buffer = mu
    []
    [mumech_init]
      type = ConstantTensor
      buffer = mumech
    []
    [disp_x]
      type = RandomTensor
      buffer = disp_x
      min = 0
      max = 0
    []
    [disp_y]
      type = RandomTensor
      buffer = disp_y
      min = 0
      max = 0
    []
    [disp_z]
      type = RandomTensor
      buffer = disp_z
      min = 0
      max = 0
    []
    [Mbar]
      type = ReciprocalLaplacianFactor
      factor = 0.2 # Mobility
      buffer = Mbar
    []
    [kappabarbar]
      type = ReciprocalLaplacianSquareFactor
      factor = -0.001 # kappa
      buffer = kappabarbar
    []
  []

  [Solve]
    [mu]
      # chemical potential (real space)
      type = ParsedCompute
      buffer = mu
      expression = '0.1*c^2*(c-1)^2' # + c*sin(x/2)*0.005'
      extra_symbols = true
      derivatives = c
      inputs = c
    []
    [mubar]
      # chemical potential (reciprocal space)
      type = ForwardFFT
      buffer = mubar
      input = mu
    []
    [mumechbar]
      # mechanical chemical potential (reciprocal space)
      type = FFTElasticChemicalPotential
      buffer = mumechbar
      cbar = cbar
      displacements = 'disp_x disp_y disp_z'
      lambda = 100
      mu = 50
      e0 = 0.02
    []
    [mumech]
      # chemical potential (reciprocal space)
      type = InverseFFT
      buffer = mumech
      input = mumechbar
    []

    [Mbarmubar]
      type = ParsedCompute
      buffer = Mbarmubar
      expression = 'Mbar*(mubar+mumechbar)'
      inputs = 'Mbar mubar mumechbar'
    []
    [cbar]
      type = ForwardFFT
      buffer = cbar
      input = c
    []

    [qsmech]
      type = FFTQuasistaticElasticity
      displacements = 'disp_x disp_y disp_z'
      cbar = cbar
      lambda = 100
      mu = 50
      e0 = 0.02
    []
  []
[]

[TensorSolver]
  type = SecantSolver
  substeps = 1
  max_iterations = 1000
  # damping = 0.75
  relative_tolerance = 1e-6
  absolute_tolerance = 1e-6
  buffer = c
  dt_epsilon = 1e-7
  reciprocal_buffer = cbar
  linear_reciprocal = kappabarbar
  nonlinear_reciprocal = Mbarmubar
  verbose = true
[]

[Postprocessors]
  [min_c]
    type = TensorExtremeValuePostprocessor
    buffer = c
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_c]
    type = TensorExtremeValuePostprocessor
    buffer = c
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []

  [min_disp_x]
    type = TensorExtremeValuePostprocessor
    buffer = disp_x
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_x]
    type = TensorExtremeValuePostprocessor
    buffer = disp_x
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []
  [min_disp_y]
    type = TensorExtremeValuePostprocessor
    buffer = disp_y
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_y]
    type = TensorExtremeValuePostprocessor
    buffer = disp_y
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []
  [min_disp_z]
    type = TensorExtremeValuePostprocessor
    buffer = disp_z
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_z]
    type = TensorExtremeValuePostprocessor
    buffer = disp_z
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []

  [C]
    type = TensorIntegralPostprocessor
    buffer = c
    execute_on = 'TIMESTEP_END'
  []
  [cavg]
    type = TensorAveragePostprocessor
    buffer = c
    execute_on = 'TIMESTEP_END'
  []
[]

[Problem]
  type = TensorProblem
[]

[Executioner]
  type = Transient
  end_time = 100
  [TimeStepper]
    type = TensorSolveIterationAdaptiveDT
    dt = 0.1
    max_iterations = 500
    min_iterations = 300
    growth_factor = 1.1
    cutback_factor = 0.9
  []
[]

[Outputs]
  csv = true
  perf_graph = true
  execute_on = 'TIMESTEP_END'
[]

(test/tests/tensor_compute/coupled_pf_mech.i)

[Domain]
  dim = 3
  nx = 128
  ny = 128
  nz = 128
  xmax = ${fparse pi*4}
  ymax = ${fparse pi*4}
  zmax = ${fparse pi*4}
  mesh_mode = DUMMY
[]

[TensorBuffers]
  # phase field
  [c]
  []
  [cbar]
  []
  [mu]
  []
  [mubar]
  []
  [Mbarmubar]
  []

  # mechanics
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [mumechbar]
  []
  [mumech]
  []

  # constant tensors
  [Mbar]
  []
  [kappabarbar]
  []
[]

[TensorOutputs]
  [xdmf]
    type = XDMFTensorOutput
    buffer = 'c disp_x disp_y disp_z mu mumech'
    output_mode = 'Node Node Node Node Cell Cell'
    enable_hdf5 = true
  []
[]

[TensorComputes]
  [Initialize]
    [c]
      type = RandomTensor
      buffer = c
      min = 0.44
      max = 0.56
    []
    [disp_x]
      type = RandomTensor
      buffer = disp_x
      min = 0
      max = 0
    []
    [disp_y]
      type = RandomTensor
      buffer = disp_y
      min = 0
      max = 0
    []
    [disp_z]
      type = RandomTensor
      buffer = disp_z
      min = 0
      max = 0
    []
    [Mbar]
      type = ReciprocalLaplacianFactor
      factor = 0.2 # Mobility
      buffer = Mbar
    []
    [kappabarbar]
      type = ReciprocalLaplacianSquareFactor
      factor = -0.001 # kappa
      buffer = kappabarbar
    []
  []

  [Solve]
    [mu]
      # chemical potential (real space)
      type = ParsedCompute
      buffer = mu
      expression = '0.1*c^2*(c-1)^2' # + c*sin(x/2)*0.005'
      extra_symbols = true
      derivatives = c
      inputs = c
    []
    [mubar]
      # chemical potential (reciprocal space)
      type = ForwardFFT
      buffer = mubar
      input = mu
    []
    [mumechbar]
      # mechanical chemical potential (reciprocal space)
      type = FFTElasticChemicalPotential
      buffer = mumechbar
      cbar = cbar
      displacements = 'disp_x disp_y disp_z'
      lambda = 100
      mu = 50
      e0 = 0.02
    []
    [mumech]
      # chemical potential (reciprocal space)
      type = InverseFFT
      buffer = mumech
      input = mumechbar
    []

    [Mbarmubar]
      type = ParsedCompute
      buffer = Mbarmubar
      expression = 'Mbar*(mubar+mumechbar)'
      inputs = 'Mbar mubar mumechbar'
    []
    [cbar]
      type = ForwardFFT
      buffer = cbar
      input = c
    []

    [qsmech]
      type = FFTQuasistaticElasticity
      displacements = 'disp_x disp_y disp_z'
      cbar = cbar
      lambda = 100
      mu = 50
      e0 = 0.02
    []
  []
[]

[TensorTimeIntegrators]
  [c]
    type = FFTSemiImplicit
    buffer = c
    reciprocal_buffer = cbar
    linear_reciprocal = kappabarbar
    nonlinear_reciprocal = Mbarmubar
  []
[]

[Postprocessors]
  [min_c]
    type = TensorExtremeValuePostprocessor
    buffer = c
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_c]
    type = TensorExtremeValuePostprocessor
    buffer = c
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []

  [min_disp_x]
    type = TensorExtremeValuePostprocessor
    buffer = disp_x
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_x]
    type = TensorExtremeValuePostprocessor
    buffer = disp_x
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []
  [min_disp_y]
    type = TensorExtremeValuePostprocessor
    buffer = disp_y
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_y]
    type = TensorExtremeValuePostprocessor
    buffer = disp_y
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []
  [min_disp_z]
    type = TensorExtremeValuePostprocessor
    buffer = disp_z
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_z]
    type = TensorExtremeValuePostprocessor
    buffer = disp_z
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []

  [C]
    type = TensorIntegralPostprocessor
    buffer = c
    execute_on = 'TIMESTEP_END'
  []
  [cavg]
    type = TensorAveragePostprocessor
    buffer = c
    execute_on = 'TIMESTEP_END'
  []
[]

[Problem]
  type = TensorProblem
  spectral_solve_substeps = 1000
  print_debug_output = true
[]

[Executioner]
  type = Transient
  num_steps = 100
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.8
    dt = 0.1
  []
  dtmax = 1000
[]

[Outputs]
  csv = true
  perf_graph = true
  execute_on = 'TIMESTEP_END'
[]

(test/tests/tensor_compute/group.i)

[Domain]
  dim = 3
  nx = 128
  ny = 128
  nz = 128
  xmax = ${fparse pi*4}
  ymax = ${fparse pi*4}
  zmax = ${fparse pi*4}
  mesh_mode = DUMMY
[]

[TensorBuffers]
  # phase field
  [c]
  []
  [cbar]
  []
  [mu]
  []
  [mubar]
  []
  [Mbarmubar]
  []

  # mechanics
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [mumechbar]
  []
  [mumech]
  []

  # constant tensors
  [Mbar]
  []
  [kappabarbar]
  []
[]

[TensorOutputs]
  [xdmf]
    type = XDMFTensorOutput
    buffer = 'c disp_x disp_y disp_z mu mumech'
    output_mode = 'Node Node Node Node Cell Cell'
    enable_hdf5 = true
  []
[]

[TensorComputes]
  [Initialize]
    [c]
      type = RandomTensor
      buffer = c
      min = 0.44
      max = 0.56
    []
    [disp_x]
      type = RandomTensor
      buffer = disp_x
      min = 0
      max = 0
    []
    [disp_y]
      type = RandomTensor
      buffer = disp_y
      min = 0
      max = 0
    []
    [disp_z]
      type = RandomTensor
      buffer = disp_z
      min = 0
      max = 0
    []
    [Mbar]
      type = ReciprocalLaplacianFactor
      factor = 0.2 # Mobility
      buffer = Mbar
    []
    [kappabarbar]
      type = ReciprocalLaplacianSquareFactor
      factor = -0.001 # kappa
      buffer = kappabarbar
    []
  []

  [Solve]
    [mu]
      # chemical potential (real space)
      type = ParsedCompute
      buffer = mu
      expression = '0.1*c^2*(c-1)^2' # + c*sin(x/2)*0.005'
      extra_symbols = true
      derivatives = c
      inputs = c
    []
    [mubar]
      # chemical potential (reciprocal space)
      type = ForwardFFT
      buffer = mubar
      input = mu
    []
    [mumechbar]
      # mechanical chemical potential (reciprocal space)
      type = FFTElasticChemicalPotential
      buffer = mumechbar
      cbar = cbar
      displacements = 'disp_x disp_y disp_z'
      lambda = 100
      mu = 50
      e0 = 0.02
    []
    [mumech]
      # chemical potential (reciprocal space)
      type = InverseFFT
      buffer = mumech
      input = mumechbar
    []

    [Mbarmubar]
      type = ParsedCompute
      buffer = Mbarmubar
      expression = 'Mbar*(mubar+mumechbar)'
      inputs = 'Mbar mubar mumechbar'
    []
    [cbar]
      type = ForwardFFT
      buffer = cbar
      input = c
    []

    [qsmech]
      type = FFTQuasistaticElasticity
      displacements = 'disp_x disp_y disp_z'
      cbar = cbar
      lambda = 100
      mu = 50
      e0 = 0.02
    []

    [group]
      type = ComputeGroup
      computes = 'cbar mumech mu mubar'
    []
  []
[]

[TensorSolver]
  type = AdamsBashforthMoulton
  buffer = c
  reciprocal_buffer = cbar
  linear_reciprocal = kappabarbar
  nonlinear_reciprocal = Mbarmubar
[]

[Postprocessors]
  [min_c]
    type = TensorExtremeValuePostprocessor
    buffer = c
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_c]
    type = TensorExtremeValuePostprocessor
    buffer = c
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []

  [min_disp_x]
    type = TensorExtremeValuePostprocessor
    buffer = disp_x
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_x]
    type = TensorExtremeValuePostprocessor
    buffer = disp_x
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []
  [min_disp_y]
    type = TensorExtremeValuePostprocessor
    buffer = disp_y
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_y]
    type = TensorExtremeValuePostprocessor
    buffer = disp_y
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []
  [min_disp_z]
    type = TensorExtremeValuePostprocessor
    buffer = disp_z
    value_type = MIN
    execute_on = 'TIMESTEP_END'
  []
  [max_disp_z]
    type = TensorExtremeValuePostprocessor
    buffer = disp_z
    value_type = MAX
    execute_on = 'TIMESTEP_END'
  []

  [C]
    type = TensorIntegralPostprocessor
    buffer = c
    execute_on = 'TIMESTEP_END'
  []
  [cavg]
    type = TensorAveragePostprocessor
    buffer = c
    execute_on = 'TIMESTEP_END'
  []
[]

[Problem]
  type = TensorProblem
  spectral_solve_substeps = 1000
  print_debug_output = true
[]

[Executioner]
  type = Transient
  num_steps = 100
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.8
    dt = 0.1
  []
  dtmax = 1000
[]

[Outputs]
  csv = true
  perf_graph = true
  execute_on = 'TIMESTEP_END'
[]

Overview
Example Input File Syntax
Input Parameters
Input Files