List of tutorials

commentnote:Before you proceed

All tutorials are written assuming that you are reasonably familiar with MOOSE. If you find most of the tutorials difficult to follow, please refer to the official MOOSE website for learning resources.

Tutorial 8: Ductile fracture

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For simplicity, we will consider a single element 3 dimensional homogeneous cube under tension. For this tutorial we will apply J2 plasticity with a linear hardening model, but in the tutorial folder you will find examples with other configurations.

elastoplasticity.i: The displacement subproblem

Similar to previous tutorials, we need to define parameters. We define additional parameters related to plasticity.

E = 6.88e4
nu = 0.33
K = '${fparse E/3/(1-2*nu)}'
G = '${fparse E/2/(1+nu)}'

sigma_y = 320
H = 3.44e3

Where H is hardening modulus and sigma_y is the yield stress.

GeneratedMeshGenerator is utilized to create a 3 dimensional cube.

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    xmax = ${a}
    ymax = ${a}
    zmax = ${a}
  []
[]

We are now transferring an additional variable to the fracture multi-app, psip_active. This is the active plastic energy. In this model active plastic energy contributes to the fracture driving energy.

[Transfers]
  [from_d]
    type = MultiAppCopyTransfer
    from_multi_app = 'fracture'
    variable = d
    source_variable = d
  []
  [to_psie_active]
    type = MultiAppCopyTransfer
    to_multi_app = 'fracture'
    variable = psie_active
    source_variable = psie_active
  []
  [to_psip_active]
    type = MultiAppCopyTransfer
    to_multi_app = 'fracture'
    variable = psip_active
    source_variable = psip_active
  []
[]

We have an additional auxiliary variable defined, F. This is a consequence of utilizing large deformation models. Previous tutorials utilized small deformation models.

[AuxVariables]
  [d]
  []
  [stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [F]
    order = CONSTANT
    family = MONOMIAL
  []
[]

Plasticity is added through constitutive updates in the Materials block.

[Materials]
  [bulk_properties]
    type = ADGenericConstantMaterial
    prop_names = 'K G l Gc psic sigma_y H'
    prop_values = '${K} ${G} ${l} ${Gc} ${psic} ${sigma_y} ${H}'
  []
  [degradation]
    type = RationalDegradationFunction
    property_name = g
    expression = (1-d)^p/((1-d)^p+(Gc/psic*xi/c0/l)*d*(1+a2*d+a2*a3*d^2))*(1-eta)+eta
    phase_field = d
    material_property_names = 'Gc psic xi c0 l '
    parameter_names = 'p a2 a3 eta '
    parameter_values = '2 -0.5 0 1e-6'
  []
  [crack_geometric]
    type = CrackGeometricFunction
    property_name = alpha
    expression = 'd'
    phase_field = d
  []
  [defgrad]
    type = ComputeDeformationGradient
  []
  [hencky]
    type = HenckyIsotropicElasticity
    bulk_modulus = K
    shear_modulus = G
    phase_field = d
    degradation_function = g
    output_properties = 'psie_active'
    outputs = exodus
  []
  [linear_hardening]
    type = LinearHardening
    phase_field = d
    yield_stress = sigma_y
    hardening_modulus = H
    degradation_function = g
    output_properties = 'psip_active'
    outputs = exodus
  []
  [J2]
    type = LargeDeformationJ2Plasticity
    hardening_model = linear_hardening
  []
  [stress]
    type = ComputeLargeDeformationStress
    elasticity_model = hencky
    plasticity_model = J2
  []
[]

Here we add the blocks for HenckyIsotropicElasticity, linearhardening, LargeDeformationJ2Plasticity, and ComputeLargeDeformationStress.

LargeDeformationJ2Plasticity: This utilizes the selected hardening model to calculate the value of the yield surface and determine whether the material has begun plastic deformation.

HenckyIsotropicElasticity: This calculates elastic stress using the hencky model. Returns the Mandel stress to ComputeLargeDeformationStress

LinearHardening:This performs plastic hardening following a linear isotropic law. It returns plastic energy to LargeDeformationJ2Plasticity

ComputeLargeDeformationStress:This computes stress given an elasticity model and a plasticity model. It uses the elasticity model to compute Cauchy stress and the plasticity model to update the plastic deformation to bring the stress state back unto the yield surface.

Modifications

The elasticity model and hardening law used can be changed.

Currently available hyperelasticity models

  1. HenckyIsotropicElasticity

  2. CNHIsotropicElasticity

Currently available hardening models

  1. ArrheniusLawHardening

  2. LinearHardening

  3. PowerLawHardening

fracture.i: The phase-field subproblem

There are two minor changes to be made to the fracture input file seen in previous tutorials.

First, we add an auxiliary variable for active plastic energy. This is to receive the value from the main app.

[AuxVariables]
  [bounds_dummy]
  []
  [psie_active]
    order = CONSTANT
    family = MONOMIAL
  []
  [psip_active]
    order = CONSTANT
    family = MONOMIAL
  []
[]

Second, we add the active plastic energy into the fracture driving energy

[Materials]
  [psi]
    type = ADDerivativeParsedMaterial
    property_name = psi
    expression = 'alpha*Gc/c0/l+g*(psie_active+psip_active)'
    coupled_variables = 'd psie_active psip_active'
    material_property_names = 'alpha(d) g(d) Gc c0 l'
    derivative_order = 1
  []
[]

Alternating Minimization

Like in previous tutorials, we rely on on MOOSE's Picard iteration to create an alternating minimization scheme.

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -snes_type'
  petsc_options_value = 'lu vinewtonrsls'

  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-10
  nl_max_its = 50

  automatic_scaling = true

  abort_on_solve_fail = true
[]