Hyperbolic Viscoplasticity Stress Update

This class uses the discrete material for a hyperbolic sine viscoplasticity model in which the effective plastic strain is solved for using a creep approach.

Description

In this numerical approach, a trial stress is calculated at the start of each simulation time increment; the trial stress calculation assumed all of the new strain increment is elastic strain:

$var element = document.getElementById("moose-equation-589e417a-0994-4667-aef4-94a10d83bea3");katex.render("\\sigma_{trial} = C_{ijkl} \\left( \\Delta \\epsilon_{assumed-elastic} + \\epsilon_{elastic}^{old} \\right)", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The algorithms checks to see if the trial stress state is outside of the yield surface, as shown in the figure to the right. If the stress state is outside of the yield surface, the algorithm recomputes the scalar effective inelastic strain required to return the stress state to the yield surface. This approach is given the name Radial Return because the yield surface used is the von Mises yield surface: in the devitoric stress space, this yield surface has the shape of a circle, and the scalar inelastic strain is assumed to always be directed at the circle center.

Recompute Iterations on the Effective Plastic Strain Increment

The recompute radial return materials each individually calculate, using the Newton Method, the amount of effective inelastic strain required to return the stress state to the yield surface.

$var element = document.getElementById("moose-equation-f747080d-307e-4977-87e9-0cec6cde5934");katex.render("\\Delta p^{(t+1)} = \\Delta p^t + d \\Delta p", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

where the change in the iterative effective inelastic strain is defined as the yield surface over the derivative of the yield surface with respect to the inelastic strain increment.

This uniaxial viscoplasticity class computes the plastic strain as a stateful material property. The constitutive equation for scalar plastic strain rate used in this model is $var element = document.getElementById("moose-equation-191e70f3-d60f-4c9d-9b3c-7e49c9068215");katex.render("\\dot{p} = \\phi (\\sigma_e , r) = \\alpha sinh \\beta (\\sigma_e -r - \\sigma_y)", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

This class is based on the implicit integration algorithm in Dunne and Petrinic (2005) pg. 162–163.

Example Input File Syntax

[./viscoplasticity]
  type = HyperbolicViscoplasticityStressUpdate
  yield_stress = 10.0
  hardening_constant = 100.0
  c_alpha = 0.2418e-6
  c_beta = 0.1135
[../]

/opt/civet/build_0/moose/modules/tensor_mechanics/test/tests/recompute_radial_return/uniaxial_viscoplasticity_incrementalstrain.i

# This is a test of the HyperbolicViscoplasticityStressUpdate model
# using the small strain formulation. The material is a visco-plastic material
# i.e. a time-dependent linear strain hardening plasticity model.
# A similar problem was run in Abaqus with exactly the same result, although the element
# used in the Abaqus simulation was a CAX4 element.  Neverthless, due to the boundary conditions
# and load, the MOOSE and Abaqus result are the same.

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

[Mesh]
  file = 1x1x1cube.e
[]

[Functions]
  [./top_pull]
    type = ParsedFunction
    value = t/100
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = SMALL
    incremental = true
    add_variables = true
    generate_output = 'stress_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
  [../]
[]

[BCs]
  [./y_pull_function]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 5
    function = top_pull
  [../]

  [./x_bot]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  [../]

  [./y_bot]
    type = DirichletBC
    variable = disp_y
    boundary = 3
    value = 0.0
  [../]

  [./z_bot]
    type = DirichletBC
    variable = disp_z
    boundary = 2
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1000.0
    poissons_ratio = 0.3
  [../]
  [./viscoplasticity]
    type = HyperbolicViscoplasticityStressUpdate
    yield_stress = 10.0
    hardening_constant = 100.0
    c_alpha = 0.2418e-6
    c_beta = 0.1135
  [../]
  [./radial_return_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = 'viscoplasticity'
    tangent_operator = elastic
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  line_search = none

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-9

  start_time = 0.0
  num_steps = 30

  dt = 1.0
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
[]

HyperbolicViscoplasticityStressUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below:

[./radial_return_stress]
  type = ComputeMultipleInelasticStress
  inelastic_models = 'viscoplasticity'
  tangent_operator = elastic
[../]

/opt/civet/build_0/moose/modules/tensor_mechanics/test/tests/recompute_radial_return/uniaxial_viscoplasticity_incrementalstrain.i

# This is a test of the HyperbolicViscoplasticityStressUpdate model
# using the small strain formulation. The material is a visco-plastic material
# i.e. a time-dependent linear strain hardening plasticity model.
# A similar problem was run in Abaqus with exactly the same result, although the element
# used in the Abaqus simulation was a CAX4 element.  Neverthless, due to the boundary conditions
# and load, the MOOSE and Abaqus result are the same.

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

[Mesh]
  file = 1x1x1cube.e
[]

[Functions]
  [./top_pull]
    type = ParsedFunction
    value = t/100
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = SMALL
    incremental = true
    add_variables = true
    generate_output = 'stress_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
  [../]
[]

[BCs]
  [./y_pull_function]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 5
    function = top_pull
  [../]

  [./x_bot]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  [../]

  [./y_bot]
    type = DirichletBC
    variable = disp_y
    boundary = 3
    value = 0.0
  [../]

  [./z_bot]
    type = DirichletBC
    variable = disp_z
    boundary = 2
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1000.0
    poissons_ratio = 0.3
  [../]
  [./viscoplasticity]
    type = HyperbolicViscoplasticityStressUpdate
    yield_stress = 10.0
    hardening_constant = 100.0
    c_alpha = 0.2418e-6
    c_beta = 0.1135
  [../]
  [./radial_return_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = 'viscoplasticity'
    tangent_operator = elastic
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  line_search = none

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-9

  start_time = 0.0
  num_steps = 30

  dt = 1.0
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
[]

Input Parameters

c_alphaViscoplasticity coefficient, scales the hyperbolic function
C++ Type:double
Options:
Description:Viscoplasticity coefficient, scales the hyperbolic function
c_betaViscoplasticity coefficient inside the hyperbolic sin function
C++ Type:double
Options:
Description:Viscoplasticity coefficient inside the hyperbolic sin function
hardening_constantHardening slope
C++ Type:double
Options:
Description:Hardening slope
yield_stressThe point at which plastic strain begins accumulating
C++ Type:double
Options:
Description:The point at which plastic strain begins accumulating

Required Parameters

absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration
Default:1e-11
C++ Type:double
Options:
Description:Absolute convergence tolerance for Newton iteration
acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
Default:10
C++ Type:double
Options:
Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
C++ Type:std::string
Options:
Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE ELEMENT SUBDOMAIN
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step
Default:0.0001
C++ Type:double
Options:
Description:The maximum inelastic strain increment allowed in a time step
relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08
C++ Type:double
Options:
Description:Relative convergence tolerance for Newton iteration

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
effective_inelastic_strain_nameeffective_plastic_strainName of the material property that stores the effective inelastic strain
Default:effective_plastic_strain
C++ Type:std::string
Options:
Description:Name of the material property that stores the effective inelastic strain
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
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

internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.
Default:False
C++ Type:bool
Options:
Description:Set true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.
internal_solve_output_onon_errorWhen to output internal Newton solve information
Default:on_error
C++ Type:MooseEnum
Options:never on_error always
Description:When to output internal Newton solve information

Debug Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Options:
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

modules/tensor_mechanics/test/tests/recompute_radial_return/uniaxial_viscoplasticity_incrementalstrain.i

modules/tensor_mechanics/test/tests/recompute_radial_return/uniaxial_viscoplasticity_incrementalstrain.i

# This is a test of the HyperbolicViscoplasticityStressUpdate model
# using the small strain formulation. The material is a visco-plastic material
# i.e. a time-dependent linear strain hardening plasticity model.
# A similar problem was run in Abaqus with exactly the same result, although the element
# used in the Abaqus simulation was a CAX4 element.  Neverthless, due to the boundary conditions
# and load, the MOOSE and Abaqus result are the same.

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

[Mesh]
  file = 1x1x1cube.e
[]

[Functions]
  [./top_pull]
    type = ParsedFunction
    value = t/100
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = SMALL
    incremental = true
    add_variables = true
    generate_output = 'stress_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
  [../]
[]

[BCs]
  [./y_pull_function]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 5
    function = top_pull
  [../]

  [./x_bot]
    type = DirichletBC
    variable = disp_x
    boundary = 4
    value = 0.0
  [../]

  [./y_bot]
    type = DirichletBC
    variable = disp_y
    boundary = 3
    value = 0.0
  [../]

  [./z_bot]
    type = DirichletBC
    variable = disp_z
    boundary = 2
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1000.0
    poissons_ratio = 0.3
  [../]
  [./viscoplasticity]
    type = HyperbolicViscoplasticityStressUpdate
    yield_stress = 10.0
    hardening_constant = 100.0
    c_alpha = 0.2418e-6
    c_beta = 0.1135
  [../]
  [./radial_return_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = 'viscoplasticity'
    tangent_operator = elastic
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  line_search = none


  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-9

  start_time = 0.0
  num_steps = 30

  dt = 1.0
[]

[Outputs]
  [./out]
    type = Exodus
    elemental_as_nodal = true
  [../]
[]

References

Fionn Dunne and Nik Petrinic. Introduction to Computational Plasticity. Oxford University Press on Demand, 2005.

@book{dunne2005introduction,
    author = "Dunne, Fionn and Petrinic, Nik",
    title = "Introduction to Computational Plasticity",
    year = "2005",
    publisher = "Oxford University Press on Demand"
}

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Example Input File Syntax
Input Parameters
Input Files
References

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