ComputeDisplacements

Compute updated displacements from the deformation gradient tensor.

Integrates a deformation gradient tensor $var element = document.getElementById("moose-equation-ee4dcd3c-9620-4d04-b6cc-de6ceccdba25");katex.render("\\mathbf{F}", element, {displayMode:false,throwOnError:false});$ to build a displacement vector. The compute first calculates the average deformation gradient tensor $var element = document.getElementById("moose-equation-53984af8-d797-4ead-b194-6b21d3d7122a");katex.render("\\mathbf{F_{box}}", element, {displayMode:false,throwOnError:false});$ , which encodes the affine diaplacement transformation $var element = document.getElementById("moose-equation-2a9b92ff-f113-475c-b425-36880c374319");katex.render("\\vec u_{aff} = (\\mathbf{F_{box}} - \\mathbf{I}) \\cdot \\vec x", element, {displayMode:false,throwOnError:false});$ . Then it subtracts the average to obtain the periodic perturtbation $var element = document.getElementById("moose-equation-26af5cc8-d918-4f22-88bf-2f64ca9ddef2");katex.render("\\mathbf{F_{per}} = \\mathbf{F}-\\mathbf{F_{box}}", element, {displayMode:false,throwOnError:false});$ , and its Fourier transform $var element = document.getElementById("moose-equation-cf9fbf4b-b3b2-414b-b852-24d22728c04a");katex.render("\\hat{\\mathbf{H}} = \\mathcal F(\\mathbf{F_{per}})", element, {displayMode:false,throwOnError:false});$ .

$var element = document.getElementById("moose-equation-7b22d15a-3908-4212-b003-3e1a695b6296");katex.render("\\hat u_{per,i} = \\sum_j \\frac{i\\vec k_j \\cdot \\hat H_{ij}}{\\vec k^2}", element, {displayMode:true,throwOnError:false});$

With $var element = document.getElementById("moose-equation-63860d06-3dbd-45d5-8615-02ad5d72e309");katex.render("\\vec u_{per} = {\\mathcal F}^{-1}(\\mathbf{\\hat{\\vec u_{per}}})", element, {displayMode:false,throwOnError:false});$ the displacement is calculated as

$var element = document.getElementById("moose-equation-4457800c-25ee-475c-8a83-d09eaa9da5df");katex.render("\\vec u = \\vec u_{aff} + \\vec u_{per}", element, {displayMode:true,throwOnError:false});$

Input Parameters

FDeformation gradient tensor.
C++ Type:std::string
Controllable:No
Description:Deformation gradient tensor.
bufferThe buffer this compute is writing to
C++ Type:std::string
Controllable:No
Description:The buffer this compute is writing to

Required 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

Visualizing displaced domains in Paraview

When using XDMF output, ensure that the "transpose" parameter is set to true (default). This counters the Paraview XDMF reader issue described here.
Add a Calculator filter with
- iHat * disp_x + jHat * disp_y + kHat * disp_z for 3d
- jHat * disp_x + kHat * disp_y for 2d (this is the part of the cooked XDMF implememntation in Paraview that the transpose can not completely fix)
Add a Warp By Vector filter to apply the result vector from the calculator as displacements

(examples/degeus_mechanics/mech.i)

[Domain]
  dim = 3
  nx = 32
  ny = 32
  nz = 32
  xmax = ${fparse 2*pi}
  ymax = ${fparse 2*pi}
  zmax = ${fparse 2*pi}
  mesh_mode = DUMMY
[]

[TensorComputes]
  [Initialize]
    [Finit]
      type = RankTwoIdentity
      buffer = F
    []

    [phase]
      type = PhaseMechanicsTest
      buffer = phase
    []
    [K]
      type = ParsedCompute
      buffer = K
      expression = '(1-phase)*Ka + phase*Kb'
      inputs = phase
      constant_names = 'Ka Kb'
      constant_expressions = '0.833 8.33'
    []
    [mu]
      type = ParsedCompute
      buffer = mu
      expression = '(1-phase)*mua + phase*mub'
      inputs = phase
      constant_names = 'mua mub'
      constant_expressions = '0.386 3.86'
    []
  []

  [Solve]
    [hyper_elasticity]
      type = HyperElasticIsotropic
      buffer = stress
      F = Fnew
      K = K
      mu = mu
    []

    [root]
      [applied_strain]
        type = MacroscopicShearTensor
        buffer = applied_strain
      []
      [mech]
        type = FFTMechanics
        buffer = Fnew
        F = F
        K = K
        mu = mu
        l_tol = 1e-2
        nl_rel_tol = 2e-2
        nl_abs_tol = 2e-2
        constitutive_model = hyper_elasticity
        stress = stress
        applied_macroscopic_strain = applied_strain
      []
    []
  []

  [Postprocess]
    [displacements]
      type = ComputeDisplacements
      buffer = disp
      F = F
    []
    [vonmises]
      type = ComputeVonMisesStress
      buffer = sV
    []
  []
[]

[TensorSolver]
  # no variables are integrated by this solver (FFTMechanics performs a steady state mechanics solve)
  type = ForwardEulerSolver
  root_compute = root
  # deformation tensor is just forwarded Fnew -> F
  forward_buffer = F
  forward_buffer_new = Fnew
  substeps = 10
[]

[TensorOutputs]
  [deformation_tensor]
    type = XDMFTensorOutput
    buffer = 'disp sV F'
    output_mode = 'OVERSIZED_NODAL CELL CELL'
    enable_hdf5 = true
  []
[]

[Executioner]
  type = Transient
  num_steps = 100
  dt = 0.01
[]

(test/tests/mechanics/mech.i)

[Domain]
  dim = 2
  nx = 32
  ny = 32
  xmax = ${fparse 2*pi}
  ymax = ${fparse 2*pi}
  zmax = ${fparse 2*pi}
  mesh_mode = DUMMY
  parallel_mode = FFT_AUTO
[]

[TensorComputes]
  [Initialize]
    [phase]
      type = ParsedCompute
      expression = '(cos(x)/2+0.5)^1*(cos(y)/2+0.5)^1*(cos(z)/2+0.5)^1'
      extra_symbols = true
      buffer = phase
    []
    [K]
      type = ParsedCompute
      buffer = K
      expression = '(1-phase)*Ka + phase*Kb'
      inputs = phase
      constant_names = 'Ka Kb'
      constant_expressions = '1 10'
    []
    [mu]
      type = ParsedCompute
      buffer = mu
      expression = '(1-phase)*mua + phase*mub'
      inputs = phase
      constant_names = 'mua mub'
      constant_expressions = '0.5 5'
    []
    [Finit]
      type = RankTwoIdentity
      buffer = F
    []
  []

  [Solve]
    [hyper_elasticity]
      type = HyperElasticIsotropic
      buffer = stress
      F = Fnew
      K = K
      mu = mu
    []

    [root]
      [applied_strain]
        type = MacroscopicShearTensor
        buffer = applied_strain
      []
      [mech]
        type = FFTMechanics
        buffer = Fnew
        F = F
        K = K
        mu = mu
        l_max_its = 40
        l_tol = 1e-5
        nl_rel_tol = 2e-4
        nl_abs_tol = 2e-3
        constitutive_model = hyper_elasticity
        stress = stress
        applied_macroscopic_strain = applied_strain
      []
    []
  []

  [Postprocess]
    [displacements]
      type = ComputeDisplacements
      buffer = disp
      F = F
    []
    [vonmises]
      type = ComputeVonMisesStress
      buffer = sV
    []
  []
[]

[TensorSolver]
  # no variables are integrated by this solver (FFTMechanics performs a steady state mechanics solve)
  type = ForwardEulerSolver
  root_compute = root
  # deformation tensor is just forwarded Fnew -> F
  forward_buffer = F
  forward_buffer_new = Fnew
  substeps = 3
[]

[TensorOutputs]
  active = 'parallel' # serial

  [serial]
    type = XDMFTensorOutput
    file_base = mech_serial
    buffer = 'disp sV F phase'
    output_mode = 'OVERSIZED_NODAL CELL CELL NODE'
    enable_hdf5 = true
    execute_on = 'TIMESTEP_END'
  []
  [parallel]
    # NODE and OVERSIZED_NODAL are not yet available in parallel output
    type = XDMFTensorOutput
    file_base = mech_parallel
    buffer = 'sV F phase'
    output_mode = 'CELL CELL CELL'
    enable_hdf5 = true
    execute_on = 'TIMESTEP_END'
  []
[]


[Executioner]
  type = Transient
  num_steps = 3
  dt = 0.02
[]

(test/tests/mechanics/mech3d.i)

[Domain]
  dim = 3
  nx = 16
  ny = 16
  nz = 16
  xmax = ${fparse 2*pi}
  ymax = ${fparse 2*pi}
  zmax = ${fparse 2*pi}
  mesh_mode = DUMMY
  parallel_mode = FFT_AUTO
[]

[TensorComputes]
  [Initialize]
    [phase]
      type = ParsedCompute
      expression = '(cos(x)/2+0.5)^1*(cos(y)/2+0.5)^1*(cos(z)/2+0.5)^1'
      extra_symbols = true
      buffer = phase
    []
    [K]
      type = ParsedCompute
      buffer = K
      expression = '(1-phase)*Ka + phase*Kb'
      inputs = phase
      constant_names = 'Ka Kb'
      constant_expressions = '1 10'
    []
    [mu]
      type = ParsedCompute
      buffer = mu
      expression = '(1-phase)*mua + phase*mub'
      inputs = phase
      constant_names = 'mua mub'
      constant_expressions = '0.5 5'
    []
    [Finit]
      type = RankTwoIdentity
      buffer = F
    []
  []

  [Solve]
    [hyper_elasticity]
      type = HyperElasticIsotropic
      buffer = stress
      F = Fnew
      K = K
      mu = mu
    []

    [root]
      [applied_strain]
        type = MacroscopicShearTensor
        buffer = applied_strain
      []
      [mech]
        type = FFTMechanics
        buffer = Fnew
        F = F
        K = K
        mu = mu
        l_tol = 1e-2
        nl_rel_tol = 2e-2
        nl_abs_tol = 2e-2
        constitutive_model = hyper_elasticity
        stress = stress
        applied_macroscopic_strain = applied_strain
      []
    []
  []

  [Postprocess]
    [displacements]
      type = ComputeDisplacements
      buffer = disp
      F = F
    []
    [vonmises]
      type = ComputeVonMisesStress
      buffer = sV
    []
  []
[]

[TensorSolver]
  # no variables are integrated by this solver (FFTMechanics performs a steady state mechanics solve)
  type = ForwardEulerSolver
  root_compute = root
  # deformation tensor is just forwarded Fnew -> F
  forward_buffer = F
  forward_buffer_new = Fnew
  substeps = 10
[]

[TensorOutputs]
  active = 'parallel' # serial

  [serial]
    type = XDMFTensorOutput
    file_base = mech3d_serial
    buffer = 'disp sV F phase'
    output_mode = 'OVERSIZED_NODAL CELL CELL NODE'
    enable_hdf5 = true
    execute_on = 'TIMESTEP_END'
  []
  [parallel]
    # NODE and OVERSIZED_NODAL are not yet available in parallel output
    type = XDMFTensorOutput
    file_base = mech3d_parallel
    buffer = 'sV F phase'
    output_mode = 'CELL CELL CELL'
    enable_hdf5 = true
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  num_steps = 3
  dt = 0.01
[]

Input Parameters
Input Files
Visualizing displaced domains in Paraview