thermomech_answer01.md

Where is coupling introduced between the thermal and mechanical solutions in this model?

The only place where coupling between the temperature and displacement solutions explicitly appears in the input file is in the block that defines the thermal eigenstrain:

[Materials<<<{"href": "../../../../syntax/Materials/index.html"}>>>]
  [expansion1]
    type = ComputeThermalExpansionEigenstrain<<<{"description": "Computes eigenstrain due to thermal expansion with a constant coefficient", "href": "../../../../source/materials/ComputeThermalExpansionEigenstrain.html"}>>>
    temperature<<<{"description": "Coupled temperature"}>>> = T
    thermal_expansion_coeff<<<{"description": "Thermal expansion coefficient"}>>> = 0.001
    stress_free_temperature<<<{"description": "Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation"}>>> = 300
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = thermal_expansion
  []
[]

In this block, the temperature parameter indicates which variable is used to define the temperature field. In this case, the T variable that is specified is a solution variable. This results in coupling between the thermal and mechanical solutions. Note that this specified variable can be either a variable that is part of the solution, as is the case here, or an auxiliary variable, which might be prescribed using a function, as was the case in the mechanics-only model that this case builds upon.

In addition to the dependency of the eigenstrain on the temperature solution, there is also a dependency of the thermal solution on the mechanical solution that is not as immediately apparent. The thermal kernels by default run on the displaced mesh, the distortion of which is computed by the mechanics models. For many models, this has a negligible effect, but it can be important in some cases, particularly when thermal contact is included.

(modules/combined/tutorials/introduction/thermal_mechanical/thermomech_step01.i)

#
# Single block coupled thermal/mechanical
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/thermoech_step01.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
  [pin]
    type = ExtraNodesetGenerator
    input = generated
    new_boundary = pin
    coord = '0 0 0'
  []
[]

[Variables]
  [T]
    initial_condition = 300.0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
    type = HeatSource
    variable = T
    value = 5e4
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    automatic_eigenstrain_names = true
    generate_output = 'vonmises_stress'
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
    specific_heat = 0.5
  []
  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000.0
  []
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [expansion1]
    type = ComputeThermalExpansionEigenstrain
    temperature = T
    thermal_expansion_coeff = 0.001
    stress_free_temperature = 300
    eigenstrain_name = thermal_expansion
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
  [pin_x]
    type = DirichletBC
    variable = disp_x
    boundary = pin
    value = 0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
[]

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

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]