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

Description:The name of the variable that this boundary condition applies to

- boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

# VectorNeumannBC

Imposes the integrated boundary condition , where is a user-defined, constant vector.

## Description

`VectorNeumannBC`

is an `IntegratedBC`

which weakly imposes the flux boundary condition , where the user specifies the vector and the unit normal vector is determined by the geometry of the domain . This class is appropriate to use in systems of partial differential equations (PDEs) of the form (1)

There is not a 1:1 correspondence between the choice of and the resulting solution, since the component of 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
[../]
```

(test/tests/bcs/misc_bcs/vector_neumann_bc_test.i)#### /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

- 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

- enableTrueSet the enabled status of the MooseObject.
Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

- 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.)

- 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.

- 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.

- seed0The seed for the master random number generator
Default:0

C++ Type:unsigned int

Options:

Description:The seed for the master random number generator

- 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.)

- 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

### Advanced Parameters

- 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

- 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

- 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

### Tagging Parameters

## Input Files

- test/tests/bcs/misc_bcs/vector_neumann_bc_test.i
- modules/tensor_mechanics/test/tests/static_deformations/beam_cosserat_02_apply_stress.i
- modules/tensor_mechanics/test/tests/static_deformations/beam_cosserat_01_slippery.i
- modules/tensor_mechanics/test/tests/static_deformations/beam_cosserat_01.i

#### 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
[]
```

#### 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 = FunctionPresetBC
variable = disp_z
boundary = left
function = '-0.3*(z*z-y*y)/2.0*1.11E-2'
[../]
[./clamp_y]
type = FunctionPresetBC
variable = disp_y
boundary = left
function = '-0.3*z*y*1.11E-2'
[../]
[./clamp_x]
type = PresetBC
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 = FunctionPresetBC
variable = wc_x
boundary = 'left' # right top bottom front back'
function = '0.3*y*1.11E-2'
[../]
[./fix_wc_y]
type = FunctionPresetBC
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_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 = PresetBC
variable = disp_y
boundary = 'bottom top'
value = 0.0
[../]
[./no_wc_y]
type = PresetBC
variable = wc_y
boundary = 'left'
value = 0.0
[../]
[./clamp_z]
type = PresetBC
variable = disp_z
boundary = left
value = 0.0
[../]
[./clamp_x]
type = PresetBC
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_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 = PresetBC
variable = disp_y
boundary = 'bottom top'
value = 0.0
[../]
[./no_wc_x]
type = PresetBC
variable = wc_x
boundary = 'bottom top back front left right'
value = 0.0
[../]
[./clamp_z]
type = PresetBC
variable = disp_z
boundary = left
value = 0.0
[../]
[./clamp_x]
type = PresetBC
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
[]
```