Plotting Yield locus

[Aayush-T]

Hi everyone,
I am new to Moose, I wanted to make a Yield surface for a biaxial loading case. I have calculated stress and strain but can not find a way for finding equivalent plastic strain. I tried using the value of stresses at t=10 sec and then calculate principal stresses from them to plot the graph for different displacement values, but the graph is not right. Can anyone help with it? The code and graph

is attached below.

[Mesh]
  type = GeneratedMesh
  dim = 2
  elem_type = QUAD4
  displacements = 'disp_x disp_y'
  nx = 1
  ny = 1
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[GlobalParams]
  volumetric_locking_correction = true
[]

[AuxVariables]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xx]
  order = CONSTANT
  family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./fp_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./gss]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./euler1]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./euler2]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./euler3]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Functions]
  [./tdisp]
    type = ParsedFunction
    value = 0.001*t
  [../]
  [./rdisp]
  type = ParsedFunction
  value = 0.001*t
[../]
[]

[UserObjects]
  [./prop_read]
    type = ElementPropertyReadFile
    prop_file_name = 'euler_ang_file.txt'
    # Enter file data as prop#1, prop#2, .., prop#nprop
    nprop = 3
    read_type = element
  [../]
[]

[AuxKernels]
  [./stress_yy]
    type = RankTwoAux
    variable = stress_yy
    rank_two_tensor = stress
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  [../]
  [./e_yy]
    type = RankTwoAux
    variable = e_yy
    rank_two_tensor = lage
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  [../]
  [./stress_xx]
    type = RankTwoAux
    variable = stress_xx
    rank_two_tensor = stress
    index_j = 0
    index_i = 0
    execute_on = timestep_end
  [../]
  [./e_xx]
    type = RankTwoAux
    variable = e_xx
    rank_two_tensor = lage
    index_j = 0
    index_i = 0
    execute_on = timestep_end
  [../]
  [./e_xy]
    type = RankTwoAux
    variable = e_xy
    rank_two_tensor = lage
    index_j = 1
    index_i = 0
    execute_on = timestep_end
  [../]
  [./stress_xy]
    type = RankTwoAux
    variable = stress_xy
    rank_two_tensor = stress
    index_j = 1
    index_i = 0
    execute_on = timestep_end
  [../]
  [./fp_yy]
    type = RankTwoAux
    variable = fp_yy
    rank_two_tensor = fp
    index_j = 1
    index_i = 1
    execute_on = timestep_end
  [../]
  [./gss]
    type = MaterialStdVectorAux
    variable = gss
    property = state_var_gss
    index = 0
    execute_on = timestep_end
  [../]
  [./euler1]
    type = MaterialRealVectorValueAux
    variable = euler1
    property = Euler_angles
    component = 0
    execute_on = timestep_end
  [../]
  [./euler2]
    type = MaterialRealVectorValueAux
    variable = euler2
    property = Euler_angles
    component = 1
    execute_on = timestep_end
  [../]
  [./euler3]
    type = MaterialRealVectorValueAux
    variable = euler3
    property = Euler_angles
    component = 2
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'bottom'
    value = 0
  [../]
  [./fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0
  [../]
  [./tdisp]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = top
    function = tdisp
  [../]
#  [./rdisp]
#    type = FunctionDirichletBC
#    variable = disp_x
#    boundary = right
#    function = rdisp
#  [../]
[]

[UserObjects]
  [./slip_rate_gss]
    type = CrystalPlasticitySlipRateGSS
    variable_size = 12
    slip_sys_file_name = input_slip_sys.txt
    num_slip_sys_flowrate_props = 2
    flowprops = '1 4 0.001 0.1 5 8 0.001 0.1 9 12 0.001 0.1'
    uo_state_var_name = state_var_gss
  [../]
  [./slip_resistance_gss]
    type = CrystalPlasticitySlipResistanceGSS
    variable_size = 12
    uo_state_var_name = state_var_gss
  [../]
  [./state_var_gss]
    type = CrystalPlasticityStateVariable
    variable_size = 12
    groups = '0 4 8 12'
    group_values = '60.8 60.8 60.8'
    uo_state_var_evol_rate_comp_name = state_var_evol_rate_comp_gss
    scale_factor = 1.0
  [../]
  [./state_var_evol_rate_comp_gss]
    type = CrystalPlasticityStateVarRateComponentGSS
    variable_size = 12
    hprops = '1.0 541.5 109.8 2.5'
    uo_slip_rate_name = slip_rate_gss
    uo_state_var_name = state_var_gss
  [../]
[]

[Materials]
  [./crysp]
    type = FiniteStrainUObasedCP
    stol = 1e-2
    tan_mod_type = exact
    uo_slip_rates = 'slip_rate_gss'
    uo_slip_resistances = 'slip_resistance_gss'
    uo_state_vars = 'state_var_gss'
    uo_state_var_evol_rate_comps = 'state_var_evol_rate_comp_gss'
  [../]
  [./strain]
    type = ComputeFiniteStrain
    displacements = 'disp_x disp_y'
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensorCP
    C_ijkl = '1.684e5 1.214e5 1.214e5 1.684e5 1.214e5 1.684e5 0.754e5 0.754e5 0.754e5'
    fill_method = symmetric9
    read_prop_user_object = prop_read
  [../]
[]

[Postprocessors]
  [./stress_yy]
    type = ElementAverageValue
    variable = stress_yy
  [../]
  [./stress_xx]
    type = ElementAverageValue
    variable = stress_xx
  [../]
  [./e_xy]
    type = ElementAverageValue
    variable = e_xy
  [../]
  [./e_yy]
    type = ElementAverageValue
    variable = e_yy
  [../]
  [./e_xx]
    type = ElementAverageValue
    variable = e_xx
  [../]
  [./stress_xy]
    type = ElementAverageValue
    variable = stress_xy
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.01
  solve_type = 'PJFNK'

  petsc_options_iname = -pc_hypre_type
  petsc_options_value = boomerang
  nl_abs_tol = 1e-10
  nl_rel_step_tol = 1e-10
  dtmax = 10.0
  nl_rel_tol = 1e-10
  dtmin = 0.01
  num_steps = 1000
  nl_abs_step_tol = 1e-10
[]

[Outputs]
  exodus = true
   csv = true
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
    use_displaced_mesh = true
  [../]
[]

[Aayush-T]

The block letter part is not part of the code and was commented by me, I forgot to remove it while pasting the code here!

[ngrilli]

Dear @Aayush-T

If you use the crystal plasticity model,
the scalar cumulative plastic strain is calculated and the variable is called "_acc_slip" in the code.
Therefore, you can add an auxiliary variable like:

[./acc_slip]
order = CONSTANT
family = MONOMIAL
[../]

and corresponding AuxKernel:

[./acc_slip]
type = MaterialRealAux
variable = acc_slip
property = acc_slip
execute_on = timestep_end
[../]

Not sure which quantity you are looking for exactly.
If you want something like Mises plastic strain, then you can output the components
of the plastic deformation gradients using for instance:

[./fp_xy]
order = CONSTANT
family = MONOMIAL
[../]

and

[./fp_xy]
type = RankTwoAux
variable = fp_xy
rank_two_tensor = fp
index_j = 1
index_i = 0
execute_on = timestep_end
[../]

Then you can calculate equivalent plastic strain with the expression you like using the paraview "calculator" filter.

Hope this helps

Best Regards,
Nicolò Grilli
National University of Singapore

[Aayush-T]

Yes, actually I was looking for ways to get the equivalent plastic strain values from the moose itself and output in the csv file as I could not find any direct function in moose that does it. Thanks for such a prompt response.

Regards,
Aayush Trivedi
IIT Bombay

[WilkAndy]

This should really be possible by setting the appropriate scalar_type in the RankTwoScalarAux . If it isn't currently possible, you (or someone), should add that functionality for future users.

[Aayush-T]

I am trying to add this. Also, the _acc_slip is not working in the dual-phase crysp case that I am using. If anyone else is able to do that, please do post or I will update it.