VectorNeumannBC

Imposes the integrated boundary condition $var element = document.getElementById("moose-equation-a17bebaf-6c06-4a63-af2b-e28056878d80");katex.render("\\frac{\\partial u}{\\partial n}=\\vec{V}\\cdot\\hat{n}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , where $var element = document.getElementById("moose-equation-a888eb15-c527-48ba-bdb6-00381ff255eb");katex.render("\\vec{V}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a user-defined, constant vector.

Description

VectorNeumannBC is an IntegratedBC which weakly imposes the flux boundary condition $var element = document.getElementById("moose-equation-52316c34-4a89-48c4-bf4c-01f2825099fb");katex.render("\\frac{\\partial u}{\\partial n} = \\vec{V}\\cdot\\hat{n}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , where the user specifies the vector $var element = document.getElementById("moose-equation-5009b449-fc46-4e93-9edf-4d344c82fb12");katex.render("\\vec{V}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and the unit normal vector $var element = document.getElementById("moose-equation-6934b7de-dc6b-4d0d-bee4-4d8b461a63c3");katex.render("\\hat{n}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is determined by the geometry of the domain $var element = document.getElementById("moose-equation-6d9268d0-3da8-4118-a5ee-c82434ba2d17");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . This class is appropriate to use in systems of partial differential equations (PDEs) of the form $var element = document.getElementById("moose-equation-58923753-8770-432b-860a-8d5dd6e12bcd");katex.render("\\begin{aligned} -\\nabla^2 u &= f && \\quad \\in \\Omega \\\\ u &= g && \\quad \\in \\partial \\Omega_D \\\\ \\frac{\\partial u}{\\partial n} &= \\vec{V} \\cdot \\hat{n} && \\quad \\in \\partial \\Omega_N \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

note

There is not a 1:1 correspondence between the choice of $var element = document.getElementById("moose-equation-c692c629-805d-4a94-a42b-8389eecbed9b");katex.render("\\vec{V}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and the resulting solution, since the component of $var element = document.getElementById("moose-equation-4de8d16e-cd31-4ebc-983c-16dc2ea95945");katex.render("\\vec{V}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ which is orthogonal to the outward normal vector will not have any effect on the result.

This class exists mainly for convenience: if the true solution has a constant flux, then it is easier to specify Neumann boundary conditions on parts of the boundary with different outward normal vectors by simply specifying the true constant flux vector, and allowing MOOSE to dot it with the appropriate outward normals as necessary.

Example Input Syntax

  [./top]
    type = VectorNeumannBC
    variable = u
    vector_value = '1 1 0'
    boundary = 2
  [../]

/opt/civet/build_0/moose/test/tests/bcs/misc_bcs/vector_neumann_bc_test.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  nz = 0
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right top'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0.0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 2.0
  [../]

  [./top]
    type = VectorNeumannBC
    variable = u
    vector_value = '1 1 0'
    boundary = 2
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

Input Parameters

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
variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this boundary condition applies to

Required Parameters

displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements
vector_value0 0 0vector this BC should act in
Default:0 0 0
C++ Type:libMesh::VectorValue
Options:
Description:vector this BC should act in

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.
diag_save_inThe name of auxiliary variables to save this BC'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
Options:
Description:The name of auxiliary variables to save this BC'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 BC'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
Options:
Description:The name of auxiliary variables to save this BC'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
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
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/tensor_mechanics/test/tests/static_deformations/beam_cosserat_01_slippery.i
modules/tensor_mechanics/test/tests/static_deformations/beam_cosserat_02_apply_stress.i
modules/tensor_mechanics/test/tests/static_deformations/beam_cosserat_01.i
test/tests/bcs/misc_bcs/vector_neumann_bc_test.i

modules/tensor_mechanics/test/tests/static_deformations/beam_cosserat_01_slippery.i

# Beam bending.  One end is clamped and the other end is subjected to
# a constant surface traction.
# The beam thickness is 1, and the Cosserat layer thickness is 0.5,
# so the beam contains 2 Cosserat layers.
# The joint normal stiffness is set very large and the shear stiffness very small
# so that the situation should be very close to a single beam of thickness
# 0.5.
# The deflection should be described by
# u_z = 2sx/G + 2s(1-nu^2)x^2(3L-x)/(Eh^2)
# wc_y = sx(x-2L)/(2B)
# Here
# s = applied shear stress = -2E-4
# x = coordinate along bar (0<=x<=10)
# G = shear modulus = E/2/(1+nu) = 0.4615
# nu = Poisson = 0.3
# L = length of bar = 10
# E = Young = 1.2
# h = Cosserat layer thickness = 0.5
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 80
  xmax = 10
  ny = 1
  nz = 1
  zmin = -0.5
  zmax = 0.5
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  Cosserat_rotations = 'wc_x wc_y wc_z'
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./wc_y]
  [../]
[]

[Kernels]
  [./cx_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_x
    component = 0
  [../]
  [./cy_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_y
    component = 1
  [../]
  [./cz_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_z
    component = 2
  [../]
  [./y_couple]
    type = StressDivergenceTensors
    variable = wc_y
    displacements = 'wc_x wc_y wc_z'
    component = 1
    base_name = couple
  [../]
  [./y_moment]
    type = MomentBalancing
    variable = wc_y
    component = 1
  [../]
[]

[BCs]
  # zmin is called back
  # zmax is called front
  # ymin is called bottom
  # ymax is called top
  # xmin is called left
  # xmax is called right
  [./no_dispy]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom top'
    value = 0.0
  [../]
  [./no_wc_y]
    type = DirichletBC
    variable = wc_y
    boundary = 'left'
    value = 0.0
  [../]
  [./clamp_z]
    type = DirichletBC
    variable = disp_z
    boundary = left
    value = 0.0
  [../]
  [./clamp_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./end_traction]
    type = VectorNeumannBC
    variable = disp_z
    vector_value = '-2E-4 0 0'
    boundary = right
  [../]
[]

[AuxVariables]
  [./wc_x]
  [../]
  [./wc_z]
  [../]
  [./strain_xx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_xy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_xz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_yx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_yy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_yz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_zx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_zy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_zz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_xx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_xy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_xz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zz]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[AuxKernels]
  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xy
    index_i = 0
    index_j = 1
  [../]
  [./strain_xz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xz
    index_i = 0
    index_j = 2
  [../]
  [./strain_yx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yx
    index_i = 1
    index_j = 0
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./strain_yz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yz
    index_i = 1
    index_j = 2
  [../]
  [./strain_zx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zx
    index_i = 2
    index_j = 0
  [../]
  [./strain_zy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zy
    index_i = 2
    index_j = 1
  [../]
  [./strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
  [../]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_xz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xz
    index_i = 0
    index_j = 2
  [../]
  [./stress_yx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yx
    index_i = 1
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yz
    index_i = 1
    index_j = 2
  [../]
  [./stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./stress_zy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zy
    index_i = 2
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]
  [./couple_stress_xx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./couple_stress_xy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./couple_stress_xz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xz
    index_i = 0
    index_j = 2
  [../]
  [./couple_stress_yx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yx
    index_i = 1
    index_j = 0
  [../]
  [./couple_stress_yy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./couple_stress_yz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yz
    index_i = 1
    index_j = 2
  [../]
  [./couple_stress_zx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./couple_stress_zy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zy
    index_i = 2
    index_j = 1
  [../]
  [./couple_stress_zz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zz
    index_i = 2
    index_j = 2
  [../]
[]

[VectorPostprocessors]
  [./soln]
    type = LineValueSampler
    sort_by = x
    variable = 'disp_x disp_z stress_xx stress_xz stress_zx stress_zz wc_y couple_stress_xx couple_stress_xz couple_stress_zx couple_stress_zz'
    start_point = '0 0 0'
    end_point = '10 0 0'
    num_points = 11
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeLayeredCosseratElasticityTensor
    young = 1.2
    poisson = 0.3
    layer_thickness = 0.5
    joint_normal_stiffness = 1E16
    joint_shear_stiffness = 1E-6
  [../]
  [./strain]
    type = ComputeCosseratSmallStrain
  [../]
  [./stress]
    type = ComputeCosseratLinearElasticStress
  [../]
[]

[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_atol -snes_rtol -snes_max_it -ksp_atol -ksp_rtol -sub_pc_factor_shift_type'
    petsc_options_value = 'gmres asm lu 1E-10 1E-14 10 1E-15 1E-10 NONZERO'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = beam_cosserat_01_slippery
  csv = true
  exodus = true
[]

modules/tensor_mechanics/test/tests/static_deformations/beam_cosserat_02_apply_stress.i

# Beam bending.
# One end is clamped and the other end is subjected to a stress
# and micromechanical moment that will induce bending.
# The stress that will induce bending around the y axis is
# stress_xx = EAz
# This implies a micromechanical moment-stress of
# m_yx = (1/12)EAh^2 for joint_shear_stiffness=0.
# For joint_shear_stiffness!=0, the micromechanical moment-stress
# is
# m_yx = (1/12)EAa^2 G/(ak_s + G)
# All other stresses and moment stresses are assumed to be zero.
# With joint_shear_stiffness=0, and introducing D=-poisson*A, the
# nonzero strains are
# ep_xx = Az
# ep_yy = Dz
# ep_zz = Dz
# kappa_xy = -D
# kappa_yx = A
# This means the displacements are:
# u_x = Axz
# u_y = Dzy
# u_z = -(A/2)x^2 + (D/2)(z^2-y^2)
# wc_x = -Dy
# wc_y = Ax
# wc_z = 0
# This is bending of a bar around the y axis, in plane stress
# (stress_yy=0).  Displacements at the left-hand (x=0) are applied
# according to the above formulae; wc_x and wc_y are applied throughout
# the bar; and stress_xx is applied at the right-hand end (x=10).
# The displacements are measured and
# compared with the above formulae.
# The test uses: E=1.2, poisson=0.3, A=1.11E-2, h=2, ks=0.1, so
# stress_xx = 1.332E-2*z
# m_yx = 0.2379E-2
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  ny = 1
  nz = 10
  xmin = 0
  xmax = 10
  ymin = -1
  ymax = 1
  zmin = -0.5
  zmax = 0.5
[]

[GlobalParams]
  #use_displaced_mesh = false
  displacements = 'disp_x disp_y disp_z'
  Cosserat_rotations = 'wc_x wc_y wc_z'
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./wc_x]
  [../]
  [./wc_y]
  [../]
[]

[Kernels]
  [./cx_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_x
    component = 0
  [../]
  [./cy_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_y
    component = 1
  [../]
  [./cz_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_z
    component = 2
  [../]
  [./x_couple]
    type = StressDivergenceTensors
    variable = wc_x
    displacements = 'wc_x wc_y wc_z'
    component = 0
    base_name = couple
  [../]
  [./y_couple]
    type = StressDivergenceTensors
    variable = wc_y
    displacements = 'wc_x wc_y wc_z'
    component = 1
    base_name = couple
  [../]
  [./x_moment]
    type = MomentBalancing
    variable = wc_x
    component = 0
  [../]
  [./y_moment]
    type = MomentBalancing
    variable = wc_y
    component = 1
  [../]
[]

[BCs]
  # zmin is called back
  # zmax is called front
  # ymin is called bottom
  # ymax is called top
  # xmin is called left
  # xmax is called right
  [./clamp_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = left
    function = '-0.3*(z*z-y*y)/2.0*1.11E-2'
  [../]
  [./clamp_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = left
    function = '-0.3*z*y*1.11E-2'
  [../]
  [./clamp_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./end_stress]
    type = FunctionNeumannBC
    boundary = right
    function = z*1.2*1.11E-2
    variable = disp_x
  [../]
  [./fix_wc_x]
    type = FunctionDirichletBC
    variable = wc_x
    boundary = 'left' # right top bottom front back'
    function = '0.3*y*1.11E-2'
  [../]
  [./fix_wc_y]
    type = FunctionDirichletBC
    variable = wc_y
    boundary = 'left' # right top bottom front back'
    function = '1.11E-2*x'
  [../]
  [./end_moment]
    type = VectorNeumannBC
    boundary = right
    variable = wc_y
    vector_value = '2.3785714286E-3 0 0'
  [../]
[]


[AuxVariables]
  [./wc_z]
  [../]
  [./strain_xx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_xy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_xz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_yx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_yy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_yz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_zx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_zy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./strain_zz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_xx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_xy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_xz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zz]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[AuxKernels]
  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xy
    index_i = 0
    index_j = 1
  [../]
  [./strain_xz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xz
    index_i = 0
    index_j = 2
  [../]
  [./strain_yx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yx
    index_i = 1
    index_j = 0
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./strain_yz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yz
    index_i = 1
    index_j = 2
  [../]
  [./strain_zx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zx
    index_i = 2
    index_j = 0
  [../]
  [./strain_zy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zy
    index_i = 2
    index_j = 1
  [../]
  [./strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
  [../]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_xz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xz
    index_i = 0
    index_j = 2
  [../]
  [./stress_yx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yx
    index_i = 1
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yz
    index_i = 1
    index_j = 2
  [../]
  [./stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./stress_zy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zy
    index_i = 2
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]
  [./couple_stress_xx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./couple_stress_xy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./couple_stress_xz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xz
    index_i = 0
    index_j = 2
  [../]
  [./couple_stress_yx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yx
    index_i = 1
    index_j = 0
  [../]
  [./couple_stress_yy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./couple_stress_yz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yz
    index_i = 1
    index_j = 2
  [../]
  [./couple_stress_zx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./couple_stress_zy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zy
    index_i = 2
    index_j = 1
  [../]
  [./couple_stress_zz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zz
    index_i = 2
    index_j = 2
  [../]
[]

[VectorPostprocessors]
  [./soln]
    type = LineValueSampler
    sort_by = x
    variable = 'disp_x disp_y disp_z stress_xx stress_xy stress_xz stress_yx stress_yy stress_yz stress_zx stress_zy stress_zz wc_x wc_y wc_z couple_stress_xx couple_stress_xy couple_stress_xz couple_stress_yx couple_stress_yy couple_stress_yz couple_stress_zx couple_stress_zy couple_stress_zz'
    start_point = '0 0 0.5'
    end_point = '10 0 0.5'
    num_points = 11
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeLayeredCosseratElasticityTensor
    young = 1.2
    poisson = 0.3
    layer_thickness = 2.0
    joint_normal_stiffness = 1E16
    joint_shear_stiffness = 0.1
  [../]
  [./strain]
    type = ComputeCosseratSmallStrain
  [../]
  [./stress]
    type = ComputeCosseratLinearElasticStress
  [../]
[]

[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_atol -snes_rtol -snes_max_it -ksp_atol -ksp_rtol -ksp_max_it -sub_pc_factor_shift_type -pc_asm_overlap -ksp_gmres_restart'
    petsc_options_value = 'gmres asm lu 1E-11 1E-11 10 1E-15 1E-10 100 NONZERO 2 100'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = beam_cosserat_02_apply_stress
  exodus = true
  csv = true
[]

modules/tensor_mechanics/test/tests/static_deformations/beam_cosserat_01.i

# Beam bending.  One end is clamped and the other end is subjected to
# a surface traction.
# The joint normal and shear stiffnesses are set very large, so
# that this situation should be identical to the standard (non-Cosserat)
# isotropic elasticity case.
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 40
  xmax = 10
  ny = 1
  nz = 4
  zmin = -0.5
  zmax = 0.5
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  Cosserat_rotations = 'wc_x wc_y wc_z'
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./wc_x]
  [../]
  [./wc_y]
  [../]
[]

[Kernels]
  [./cx_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_x
    component = 0
  [../]
  [./cy_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_y
    component = 1
  [../]
  [./cz_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_z
    component = 2
  [../]
  [./x_couple]
    type = StressDivergenceTensors
    variable = wc_x
    displacements = 'wc_x wc_y wc_z'
    component = 0
    base_name = couple
  [../]
  [./y_couple]
    type = StressDivergenceTensors
    variable = wc_y
    displacements = 'wc_x wc_y wc_z'
    component = 1
    base_name = couple
  [../]
  [./x_moment]
    type = MomentBalancing
    variable = wc_x
    component = 0
  [../]
  [./y_moment]
    type = MomentBalancing
    variable = wc_y
    component = 1
  [../]
[]

[BCs]
  # zmin is called back
  # zmax is called front
  # ymin is called bottom
  # ymax is called top
  # xmin is called left
  # xmax is called right
  [./no_dispy]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom top'
    value = 0.0
  [../]
  [./no_wc_x]
    type = DirichletBC
    variable = wc_x
    boundary = 'bottom top back front left right'
    value = 0.0
  [../]
  [./clamp_z]
    type = DirichletBC
    variable = disp_z
    boundary = left
    value = 0.0
  [../]
  [./clamp_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./end_traction]
    type = VectorNeumannBC
    variable = disp_z
    vector_value = '-2E-4 0 0'
    boundary = right
  [../]
[]

[AuxVariables]
  [./wc_z]
  [../]
  [./stress_xx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_xy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_xz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_yz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./stress_zz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_xz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_yz]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zx]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zy]
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./couple_stress_zz]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_xz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xz
    index_i = 0
    index_j = 2
  [../]
  [./stress_yx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yx
    index_i = 1
    index_j = 0
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_yz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yz
    index_i = 1
    index_j = 2
  [../]
  [./stress_zx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./stress_zy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zy
    index_i = 2
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]
  [./couple_stress_xx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./couple_stress_xy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./couple_stress_xz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_xz
    index_i = 0
    index_j = 2
  [../]
  [./couple_stress_yx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yx
    index_i = 1
    index_j = 0
  [../]
  [./couple_stress_yy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./couple_stress_yz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_yz
    index_i = 1
    index_j = 2
  [../]
  [./couple_stress_zx]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zx
    index_i = 2
    index_j = 0
  [../]
  [./couple_stress_zy]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zy
    index_i = 2
    index_j = 1
  [../]
  [./couple_stress_zz]
    type = RankTwoAux
    rank_two_tensor = couple_stress
    variable = couple_stress_zz
    index_i = 2
    index_j = 2
  [../]
[]

[VectorPostprocessors]
  [./soln]
    type = LineValueSampler
    sort_by = x
    variable = 'disp_x disp_z stress_xx stress_xz stress_zx stress_zz wc_x wc_y  couple_stress_xx couple_stress_xz couple_stress_zx couple_stress_zz'
    start_point = '0 0 0.5'
    end_point = '10 0 0.5'
    num_points = 11
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeLayeredCosseratElasticityTensor
    young = 1.2
    poisson = 0.3
    layer_thickness = 1
    joint_normal_stiffness = 1E16
    joint_shear_stiffness = 1E16
  [../]
  [./strain]
    type = ComputeCosseratSmallStrain
  [../]
  [./stress]
    type = ComputeCosseratLinearElasticStress
  [../]
[]

[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -sub_pc_type -snes_atol -snes_rtol -snes_max_it -ksp_atol -ksp_rtol -sub_pc_factor_shift_type'
    petsc_options_value = 'gmres asm lu 1E-10 1E-14 10 1E-15 1E-10 NONZERO'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = beam_cosserat_01
  csv = true
  exodus = true
[]

test/tests/bcs/misc_bcs/vector_neumann_bc_test.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  nz = 0
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  active = 'diff'

  [./diff]
    type = Diffusion
    variable = u
  [../]
[]

[BCs]
  active = 'left right top'

  [./left]
    type = DirichletBC
    variable = u
    boundary = 3
    value = 0.0
  [../]

  [./right]
    type = DirichletBC
    variable = u
    boundary = 1
    value = 2.0
  [../]

  [./top]
    type = VectorNeumannBC
    variable = u
    vector_value = '1 1 0'
    boundary = 2
  [../]
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

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