PorousFlowPlasticHeatEnergy

Plastic heat energy density source = (1 - porosity) * coeff * stress * plastic_strain_rate

This Kernel implements the weak form of $var element = document.getElementById("moose-equation-e4dc01ed-b9d8-4be3-a674-73a29d131507");katex.render(" -\\nu (1-\\phi)\\sigma^{\\mathrm{eff}}_{ij}\\frac{\\partial}{\\partial t}\\epsilon_{ij}^{\\mathrm{plastic}}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where all parameters are defined in the nomenclature. Hence, this Kernel models the heating produced by inelastic deformation of the porous skeleton.

Some examples may be found in the test descriptions

Input Parameters

PorousFlowDictatorThe UserObject that holds the list of PorousFlow variable names.
C++ Type:UserObjectName
Options:
Description:The UserObject that holds the list of PorousFlow variable names.
displacementsThe string of displacements suitable for the problem statement
C++ Type:std::vector<VariableName>
Options:
Description:The string of displacements suitable for the problem statement
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this residual object operates on

Required Parameters

base_nameMaterial property base name
C++ Type:std::string
Options:
Description:Material property base name
blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector<SubdomainName>
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
coeff1Heat energy density = coeff * stress * plastic_strain_rate
Default:1
C++ Type:double
Options:
Description:Heat energy density = coeff * stress * plastic_strain_rate
strain_at_nearest_qpFalseWhen calculating nodal porosity that depends on strain, use the strain at the nearest quadpoint. This adds a small extra computational burden, and is not necessary for simulations involving only linear lagrange elements. If you set this to true, you will also want to set the same parameter to true for related Kernels and Materials
Default:False
C++ Type:bool
Options:
Description:When calculating nodal porosity that depends on strain, use the strain at the nearest quadpoint. This adds a small extra computational burden, and is not necessary for simulations involving only linear lagrange elements. If you set this to true, you will also want to set the same parameter to true for related Kernels and Materials

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
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
Options:
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.

Advanced Parameters

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Options:
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

(modules/porous_flow/test/tests/jacobian/phe01.i)
(modules/porous_flow/test/tests/plastic_heating/shear01.i)
(modules/porous_flow/test/tests/plastic_heating/compressive01.i)
(modules/porous_flow/test/tests/plastic_heating/tensile01.i)

(modules/porous_flow/test/tests/jacobian/phe01.i)

# Capped weak-plane plasticity, Kernel = PorousFlowPlasticHeatEnergy
[Mesh]
  type = GeneratedMesh
  dim = 3
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  PorousFlowDictator = dictator
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temperature]
  []
[]

[ICs]
  [disp_x]
    type = RandomIC
    variable = disp_x
    min = -0.1
    max = 0.1
  []
  [disp_y]
    type = RandomIC
    variable = disp_y
    min = -0.1
    max = 0.1
  []
  [disp_z]
    type = RandomIC
    variable = disp_z
    min = -0.1
    max = 0.1
  []
  [temp]
    type = RandomIC
    variable = temperature
    min = 0.1
    max = 0.2
  []
[]

[Kernels]
  [phe]
    type = PorousFlowPlasticHeatEnergy
    variable = temperature
  []
  [dummy_disp_x]
    type = PorousFlowPlasticHeatEnergy
    coeff = -1.3
    variable = disp_x
  []
  [dummy_disp_y]
    type = PorousFlowPlasticHeatEnergy
    coeff = 1.1
    variable = disp_y
  []
  [dummy_disp_z]
    type = PorousFlowPlasticHeatEnergy
    coeff = 0.2
    variable = disp_z
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = 'temperature disp_x disp_y disp_z'
    number_fluid_phases = 0
    number_fluid_components = 0
  []
  [coh]
    type = TensorMechanicsHardeningExponential
    value_0 = 1
    value_residual = 2
    rate = 1
  []
  [tanphi]
    type = TensorMechanicsHardeningExponential
    value_0 = 1.0
    value_residual = 0.5
    rate = 2
  []
  [tanpsi]
    type = TensorMechanicsHardeningExponential
    value_0 = 0.1
    value_residual = 0.05
    rate = 3
  []
  [t_strength]
    type = TensorMechanicsHardeningExponential
    value_0 = 100
    value_residual = 100
    rate = 1
  []
  [c_strength]
    type = TensorMechanicsHardeningCubic
    value_0 = 1
    value_residual = 0
    internal_0 = -2
    internal_limit = 0
  []
[]

[Materials]
  [temp]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [porosity]
    type = PorousFlowPorosity
    thermal = true
    mechanical = true
    porosity_zero = 0.3
    thermal_expansion_coeff = 1.3
  []
  [volstrain]
    type = PorousFlowVolumetricStrain
  []
  [phe]
    type = ComputePlasticHeatEnergy
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    lambda = 1.0
    shear_modulus = 2.0
  []
  [strain]
    type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y disp_z'
    eigenstrain_names = ini_stress
  []
  [ini_stress]
    type = ComputeEigenstrainFromInitialStress
    initial_stress = '0 0 0  0 0 1  0 1 -1.5'
    eigenstrain_name = ini_stress
  []
  [admissible]
    type = ComputeMultipleInelasticStress
    inelastic_models = mc
    tangent_operator = nonlinear
  []
  [mc]
    type = CappedWeakPlaneStressUpdate
    cohesion = coh
    tan_friction_angle = tanphi
    tan_dilation_angle = tanpsi
    tensile_strength = t_strength
    compressive_strength = c_strength
    max_NR_iterations = 20
    tip_smoother = 0
    smoothing_tol = 1
    yield_function_tol = 1E-10
    perfect_guess = false
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -snes_type'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000 test'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
[]

(modules/porous_flow/test/tests/plastic_heating/shear01.i)

# Tensile heating, using capped weak-plane plasticity
# x_disp(z=1) = t
# totalstrain_xz = t
# with C_ijkl = 0.5 0.25
# stress_zx = stress_xz = 0.25*t, so q=0.25*t, but
# with cohesion=1 and tan(phi)=1: max(q)=1.  With tan(psi)=0,
# the plastic return is always to (p, q) = (0, 1),
# so plasticstrain_zx = max(t - 4, 0)
# heat_energy_rate = coeff * (t - 4) for t>4
# Heat capacity of rock = specific_heat_cap * density = 4
# So temperature of rock should be:
# (1 - porosity) * 4 * T = (1 - porosity) * coeff * (t - 4)
[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = -10
  xmax = 10
  zmin = 0
  zmax = 1
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  PorousFlowDictator = dictator
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [energy_dot]
    type = PorousFlowEnergyTimeDerivative
    variable = temperature
  []
  [phe]
    type = PorousFlowPlasticHeatEnergy
    variable = temperature
    coeff = 8
  []
[]

[AuxVariables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxKernels]
  [disp_x]
    type = FunctionAux
    variable = disp_x
    function = 'z*t'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = temperature
    number_fluid_phases = 0
    number_fluid_components = 0
  []
  [coh]
    type = TensorMechanicsHardeningConstant
    value = 1
  []
  [tanphi]
    type = TensorMechanicsHardeningConstant
    value = 1.0
  []
  [tanpsi]
    type = TensorMechanicsHardeningConstant
    value = 0.0
  []
  [t_strength]
    type = TensorMechanicsHardeningConstant
    value = 10
  []
  [c_strength]
    type = TensorMechanicsHardeningConstant
    value = 10
  []
[]

[Materials]
  [rock_internal_energy]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 2
    density = 2
  []
  [temp]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.7
  []
  [phe]
    type = ComputePlasticHeatEnergy
  []
  [elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = symmetric_isotropic
    C_ijkl = '0.5 0.25'
  []
  [strain]
    type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y disp_z'
  []
  [admissible]
    type = ComputeMultipleInelasticStress
    inelastic_models = mc
    perform_finite_strain_rotations = false
  []
  [mc]
    type = CappedWeakPlaneStressUpdate
    cohesion = coh
    tan_friction_angle = tanphi
    tan_dilation_angle = tanpsi
    tensile_strength = t_strength
    compressive_strength = c_strength
    tip_smoother = 0
    smoothing_tol = 1
    yield_function_tol = 1E-10
    perfect_guess = true
  []
[]

[Postprocessors]
  [temp]
    type = PointValue
    point = '0 0 0'
    variable = temperature
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 10
[]

[Outputs]
  file_base = shear01
  csv = true
[]

(modules/porous_flow/test/tests/plastic_heating/compressive01.i)

# Tensile heating, using capped weak-plane plasticity
# z_disp(z=1) = -t
# totalstrain_zz = -t
# with C_ijkl = 0.5 0.25
# stress_zz = -t, but with compressive_strength = 1, stress_zz = max(-t, -1)
# so plasticstrain_zz = -(t - 1)
# heat_energy_rate = coeff * (t - 1)
# Heat capacity of rock = specific_heat_cap * density = 4
# So temperature of rock should be:
# (1 - porosity) * 4 * T = (1 - porosity) * coeff * (t - 1)
[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = -10
  xmax = 10
  zmin = 0
  zmax = 1
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  PorousFlowDictator = dictator
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [energy_dot]
    type = PorousFlowEnergyTimeDerivative
    variable = temperature
  []
  [phe]
    type = PorousFlowPlasticHeatEnergy
    variable = temperature
  []
[]

[AuxVariables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxKernels]
  [disp_z]
    type = FunctionAux
    variable = disp_z
    function = '-z*t'
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = temperature
    number_fluid_phases = 0
    number_fluid_components = 0
  []
  [coh]
    type = TensorMechanicsHardeningConstant
    value = 100
  []
  [tanphi]
    type = TensorMechanicsHardeningConstant
    value = 1.0
  []
  [t_strength]
    type = TensorMechanicsHardeningConstant
    value = 1
  []
  [c_strength]
    type = TensorMechanicsHardeningConstant
    value = 1
  []
[]

[Materials]
  [rock_internal_energy]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 2
    density = 2
  []
  [temp]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [phe]
    type = ComputePlasticHeatEnergy
  []
  [elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = symmetric_isotropic
    C_ijkl = '0.5 0.25'
  []
  [strain]
    type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y disp_z'
  []
  [admissible]
    type = ComputeMultipleInelasticStress
    inelastic_models = mc
    perform_finite_strain_rotations = false
  []
  [mc]
    type = CappedWeakPlaneStressUpdate
    cohesion = coh
    tan_friction_angle = tanphi
    tan_dilation_angle = tanphi
    tensile_strength = t_strength
    compressive_strength = c_strength
    tip_smoother = 0
    smoothing_tol = 1
    yield_function_tol = 1E-10
    perfect_guess = true
  []
[]

[Postprocessors]
  [temp]
    type = PointValue
    point = '0 0 0'
    variable = temperature
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 10
[]

[Outputs]
  file_base = compressive01
  csv = true
[]

(modules/porous_flow/test/tests/plastic_heating/tensile01.i)

# Tensile heating, using capped weak-plane plasticity
# z_disp(z=1) = t
# totalstrain_zz = t
# with C_ijkl = 0.5 0.25
# stress_zz = t, but with tensile_strength = 1, stress_zz = min(t, 1)
# so plasticstrain_zz = t - 1
# heat_energy_rate = coeff * (t - 1)
# Heat capacity of rock = specific_heat_cap * density = 4
# So temperature of rock should be:
# (1 - porosity) * 4 * T = (1 - porosity) * coeff * (t - 1)
[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = -10
  xmax = 10
  zmin = 0
  zmax = 1
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  PorousFlowDictator = dictator
[]

[Variables]
  [temperature]
  []
[]

[Kernels]
  [energy_dot]
    type = PorousFlowEnergyTimeDerivative
    variable = temperature
  []
  [phe]
    type = PorousFlowPlasticHeatEnergy
    variable = temperature
  []
[]

[AuxVariables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[AuxKernels]
  [disp_z]
    type = FunctionAux
    variable = disp_z
    function = z*t
  []
[]

[UserObjects]
  [dictator]
    type = PorousFlowDictator
    porous_flow_vars = temperature
    number_fluid_phases = 0
    number_fluid_components = 0
  []
  [coh]
    type = TensorMechanicsHardeningConstant
    value = 100
  []
  [tanphi]
    type = TensorMechanicsHardeningConstant
    value = 1.0
  []
  [t_strength]
    type = TensorMechanicsHardeningConstant
    value = 1
  []
  [c_strength]
    type = TensorMechanicsHardeningConstant
    value = 1
  []
[]

[Materials]
  [rock_internal_energy]
    type = PorousFlowMatrixInternalEnergy
    specific_heat_capacity = 2
    density = 2
  []
  [temp]
    type = PorousFlowTemperature
    temperature = temperature
  []
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.2
  []
  [phe]
    type = ComputePlasticHeatEnergy
  []
  [elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = symmetric_isotropic
    C_ijkl = '0.5 0.25'
  []
  [strain]
    type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y disp_z'
  []
  [admissible]
    type = ComputeMultipleInelasticStress
    inelastic_models = mc
    perform_finite_strain_rotations = false
  []
  [mc]
    type = CappedWeakPlaneStressUpdate
    cohesion = coh
    tan_friction_angle = tanphi
    tan_dilation_angle = tanphi
    tensile_strength = t_strength
    compressive_strength = c_strength
    tip_smoother = 0
    smoothing_tol = 1
    yield_function_tol = 1E-10
    perfect_guess = true
  []
[]

[Postprocessors]
  [temp]
    type = PointValue
    point = '0 0 0'
    variable = temperature
  []
[]

[Preconditioning]
  [andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it'
    petsc_options_value = 'bcgs bjacobi 1E-15 1E-10 10000'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  dt = 1
  end_time = 10
[]

[Outputs]
  file_base = tensile01
  csv = true
[]

Input Parameters
Input Files

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