ComputeWeightedGapCartesianLMMechanicalContact

The Karush-Kuhn-Tucker conditions of mechanical contact are:

$var element = document.getElementById("moose-equation-84a3f5cc-99b6-4c50-bf0d-259a132cbe52");katex.render("\\begin{aligned} g &\\ge 0\\\\ \\lambda &\\ge 0\\\\ g\\lambda &= 0 \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-0110b6f8-6f6f-4e30-a9d1-fe3afe53a2bb");katex.render("g", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the gap and $var element = document.getElementById("moose-equation-caba853e-6e0b-4d84-8318-c31390d1a60e");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the contact pressure, a Lagrange multiplier variable living on the secondary face. Per (Wohlmuth, 2011) and (Popp and Wall, 2014), the variationally consistent, discretized version of the KKT conditions are:

$var element = document.getElementById("moose-equation-07c2ce65-989c-4d28-aa3a-ac48f5b2cd7c");katex.render("\\begin{aligned} (\\tilde{g}_n)_j &\\ge 0\\\\ (\\lambda_n)_j &\\ge 0\\\\ (\\tilde{g}_n)_j (\\lambda_n)_j &= 0 \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-5c8e8beb-3067-441e-9cc7-42a41d5ed9d8");katex.render("n", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ indicates the normal direction, $var element = document.getElementById("moose-equation-94229132-070b-4bad-a197-d5465d93944f");katex.render("j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denotes the j'th secondary contact interface node, and $var element = document.getElementById("moose-equation-480b6f0f-5013-4c8f-a0f8-2c750bda26d0");katex.render("(\\tilde{g}_n)_j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the discrete weighted gap, computed by:

$var element = document.getElementById("moose-equation-543da4ea-7005-468c-8cc8-6870986c0512");katex.render("(\\tilde{g}_n)_j = \\int_{\\gamma_c^{(1)}} \\Phi_j g_{n,h} dA", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-d65121e1-a8b1-4b36-9502-547476818dd6");katex.render("\\gamma_c^{(1)}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denotes the secondary contact interface, $var element = document.getElementById("moose-equation-1758f7f3-62be-4564-a6ac-1687aad88ed0");katex.render("\\Phi_j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the j'th lagrange multiplier test function, and $var element = document.getElementById("moose-equation-561d4d2d-dd64-4668-990d-8dbdc60aab7a");katex.render("g_{n,h}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the discretized version of the gap function.

The KKT conditions are enforced using a nonlinear complementarity problem (NCP) function, in this case the most simple such function, $var element = document.getElementById("moose-equation-e204033b-9128-4a51-b0ac-ee77b17d43f7");katex.render("min(c(\\tilde{g}_n)_j, (\\lambda_n)_j)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , where $var element = document.getElementById("moose-equation-ec933b65-c8a9-499e-8f6a-9ed7cf3d59d4");katex.render("c", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (implemented with the input parameter c) is used to balance the size of the gap and the normal contact pressure. If the contact pressure is of order 10000, and the gap is of order .01, then c should be set to 1e6 in order to bring components of the NCP function onto the same level and achieve optimal convergence in the non-linear solve.

The ComputeWeightedGapCartesianLMMechanicalContact object computes the weighted gap and applies the KKT conditions using Lagrange multipliers defined in a global Cartesian reference frame. As a consequence, the number of contact constraints at each node will be two, in two-dimensional problems, and three, in three-dimensional problems. The normal contact pressure is obtained by projecting the Lagrange multiplier vector along the normal vector computed from the mortar generation objects. The result is a normal contact constraint, which, in general, will be a function of all (two or three) Cartesian Lagrange multipliers. This methodology only constrains one degree of freedom. The other degree(s) of freedom are constrained by enforcing that tangential tractions are identically zero. Note that, if friction with Cartesian Lagrange multipliers is chosen via ComputeFrictionalForceCartesianLMMechanicalContact, those remaining nodal degrees of freedom are constraint using Coulomb constraints within a semi-smooth Newton approach. Usage of Cartesian Lagrange multipliers is recommended when condensing Lagrange multipliers via the variable condensation preconditioner (VCP) VariableCondensationPreconditioner.

The user can also employ locally oriented Lagrange multipliers ComputeWeightedGapLMMechanicalContact, which minimizes the number of contact constraints for frictionless problems.

Computes the weighted gap that will later be used to enforce the zero-penetration mechanical contact conditions

Input Parameters

disp_xThe x displacement variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The x displacement variable
disp_yThe y displacement variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The y displacement variable
lm_xMechanical contact Lagrange multiplier along the x Cartesian axis
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Mechanical contact Lagrange multiplier along the x Cartesian axis
lm_yMechanical contact Lagrange multiplier along the y Cartesian axis.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Mechanical contact Lagrange multiplier along the y Cartesian axis.
primary_boundaryThe name of the primary boundary sideset.
C++ Type:BoundaryName
Unit:(no unit assumed)
Controllable:No
Description:The name of the primary boundary sideset.
primary_subdomainThe name of the primary subdomain.
C++ Type:SubdomainName
Unit:(no unit assumed)
Controllable:No
Description:The name of the primary subdomain.
secondary_boundaryThe name of the secondary boundary sideset.
C++ Type:BoundaryName
Unit:(no unit assumed)
Controllable:No
Description:The name of the secondary boundary sideset.
secondary_subdomainThe name of the secondary subdomain.
C++ Type:SubdomainName
Unit:(no unit assumed)
Controllable:No
Description:The name of the secondary subdomain.

Required Parameters

aux_lmAuxiliary Lagrange multiplier variable that is utilized together with the Petrov-Galerkin approach.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Auxiliary Lagrange multiplier variable that is utilized together with the Petrov-Galerkin approach.
c1e+06Parameter for balancing the size of the gap and contact pressure
Default:1e+06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Parameter for balancing the size of the gap and contact pressure
compute_lm_residualsTrueWhether to compute Lagrange Multiplier residuals
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to compute Lagrange Multiplier residuals
compute_primal_residualsTrueWhether to compute residuals for the primal variable.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to compute residuals for the primal variable.
correct_edge_droppingFalseWhether to enable correct edge dropping treatment for mortar constraints. When disabled any Lagrange Multiplier degree of freedom on a secondary element without full primary contributions will be set (strongly) to 0.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to enable correct edge dropping treatment for mortar constraints. When disabled any Lagrange Multiplier degree of freedom on a secondary element without full primary contributions will be set (strongly) to 0.
debug_meshFalseWhether this constraint is going to enable mortar segment mesh debug information. An exodusfile will be generated if the user sets this flag to true
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether this constraint is going to enable mortar segment mesh debug information. An exodusfile will be generated if the user sets this flag to true
disp_zThe z displacement variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The z displacement variable
ghost_higher_d_neighborsFalseWhether we should ghost higher-dimensional neighbors. This is necessary when we are doing second order mortar with finite volume primal variables, because in order for the method to be second order we must use cell gradients, which couples in the neighbor cells.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether we should ghost higher-dimensional neighbors. This is necessary when we are doing second order mortar with finite volume primal variables, because in order for the method to be second order we must use cell gradients, which couples in the neighbor cells.
ghost_point_neighborsFalseWhether we should ghost point neighbors of secondary face elements, and consequently also their mortar interface couples.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether we should ghost point neighbors of secondary face elements, and consequently also their mortar interface couples.
interpolate_normalsFalseWhether to interpolate the nodal normals (e.g. classic idea of evaluating field at quadrature points). If this is set to false, then non-interpolated nodal normals will be used, and then the _normals member should be indexed with _i instead of _qp
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to interpolate the nodal normals (e.g. classic idea of evaluating field at quadrature points). If this is set to false, then non-interpolated nodal normals will be used, and then the _normals member should be indexed with _i instead of _qp
lm_zMechanical contact Lagrange multiplier along the z Cartesian axis.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Mechanical contact Lagrange multiplier along the z Cartesian axis.
minimum_projection_angle40Parameter to control which angle (in degrees) is admissible for the creation of mortar segments. If set to a value close to zero, very oblique projections are allowed, which can result in mortar segments solving physics not meaningfully, and overprojection of primary nodes onto the mortar segment mesh in extreme cases. This parameter is mostly intended for mortar mesh debugging purposes in two dimensions.
Default:40
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Parameter to control which angle (in degrees) is admissible for the creation of mortar segments. If set to a value close to zero, very oblique projections are allowed, which can result in mortar segments solving physics not meaningfully, and overprojection of primary nodes onto the mortar segment mesh in extreme cases. This parameter is mostly intended for mortar mesh debugging purposes in two dimensions.
normalize_cFalseWhether to normalize c by weighting function norm. When unnormalized the value of c effectively depends on element size since in the constraint we compare nodal Lagrange Multiplier values to integrated gap values (LM nodal value is independent of element size, where integrated values are dependent on element size).
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to normalize c by weighting function norm. When unnormalized the value of c effectively depends on element size since in the constraint we compare nodal Lagrange Multiplier values to integrated gap values (LM nodal value is independent of element size, where integrated values are dependent on element size).
periodicFalseWhether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector for projection from outward to inward facing
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector for projection from outward to inward facing
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
quadratureDEFAULTQuadrature rule to use on mortar segments. For 2D mortar DEFAULT is recommended. For 3D mortar, QUAD meshes are integrated using triangle mortar segments. While DEFAULT quadrature order is typically sufficiently accurate, exact integration of QUAD mortar faces requires SECOND order quadrature for FIRST variables and FOURTH order quadrature for SECOND order variables.
Default:DEFAULT
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:DEFAULT, FIRST, SECOND, THIRD, FOURTH
Controllable:No
Description:Quadrature rule to use on mortar segments. For 2D mortar DEFAULT is recommended. For 3D mortar, QUAD meshes are integrated using triangle mortar segments. While DEFAULT quadrature order is typically sufficiently accurate, exact integration of QUAD mortar faces requires SECOND order quadrature for FIRST variables and FOURTH order quadrature for SECOND order variables.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
use_petrov_galerkinFalseWhether to use the Petrov-Galerkin approach for the mortar-based constraints. If set to true, we use the standard basis as the test function and dual basis as the shape function for the interpolation of the Lagrange multiplier variable.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to use the Petrov-Galerkin approach for the mortar-based constraints. If set to true, we use the standard basis as the test function and dual basis as the shape function for the interpolation of the Lagrange multiplier variable.
variableThe name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Unit:(no unit assumed)
Controllable:No
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<TagName>
Unit:(no unit assumed)
Controllable:No
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
Unit:(no unit assumed)
Options:nontime, system
Controllable:No
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
Unit:(no unit assumed)
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:Yes
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
Unit:(no unit assumed)
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshTrueWhether 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:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
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

Input Files

(modules/contact/test/tests/mortar_cartesian_lms/frictionless-mortar-3d.i)
(modules/contact/test/tests/mortar_cartesian_lms/frictionless-weighted-gap-lm.i)
(modules/contact/test/tests/mortar_cartesian_lms/two_block_1st_order_constraint_lm_xy.i)
(modules/contact/test/tests/mortar_aux_kernels/pressure-aux-frictionless-3d.i)
(modules/contact/test/tests/mortar_aux_kernels/pressure-aux-frictionless.i)

Child Objects

(modules/contact/include/constraints/ComputeFrictionalForceCartesianLMMechanicalContact.h)

References

Alexander Popp and WA Wall. Dual mortar methods for computational contact mechanics–overview and recent developments. GAMM-Mitteilungen, 37(1):66–84, 2014.

@article{popp2014dual,
    author = "Popp, Alexander and Wall, WA",
    title = "Dual mortar methods for computational contact mechanics--overview and recent developments",
    journal = "GAMM-Mitteilungen",
    volume = "37",
    number = "1",
    pages = "66--84",
    year = "2014",
    publisher = "Wiley Online Library"
}

Barbara Wohlmuth. Variationally consistent discretization schemes and numerical algorithms for contact problems. Acta Numerica, 20:569–734, 2011.

@article{wohlmuth2011variationally,
    author = "Wohlmuth, Barbara",
    title = "Variationally consistent discretization schemes and numerical algorithms for contact problems",
    journal = "Acta Numerica",
    volume = "20",
    pages = "569--734",
    year = "2011",
    publisher = "Cambridge University Press"
}

(modules/contact/test/tests/mortar_cartesian_lms/frictionless-mortar-3d.i)

starting_point = 0.25
offset = 0.00

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  diffusivity = 1e0
  scaling = 1e0
[]

[Mesh]
  second_order = false
  [top_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 3
    nz = 3
    xmin = -0.25
    xmax = 0.25
    ymin = -0.25
    ymax = 0.25
    zmin = -0.25
    zmax = 0.25
    elem_type = HEX8
  []
  [rotate_top_block]
    type = TransformGenerator
    input = top_block
    transform = ROTATE
    vector_value = '0 0 0'
  []
  [top_block_sidesets]
    type = RenameBoundaryGenerator
    input = rotate_top_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = 'top_bottom top_back top_right top_front top_left top_top'
  []
  [top_block_id]
    type = SubdomainIDGenerator
    input = top_block_sidesets
    subdomain_id = 1
  []
  [bottom_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 10
    nz = 2
    xmin = -.5
    xmax = .5
    ymin = -.5
    ymax = .5
    zmin = -.3
    zmax = -.25
    elem_type = HEX8
  []
  [bottom_block_id]
    type = SubdomainIDGenerator
    input = bottom_block
    subdomain_id = 2
  []
  [bottom_block_change_boundary_id]
    type = RenameBoundaryGenerator
    input = bottom_block_id
    old_boundary = '0 1 2 3 4 5'
    new_boundary = '100 101 102 103 104 105'
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'top_block_id bottom_block_change_boundary_id'
  []
  [block_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'top_block bottom_block'
  []
  [bottom_right_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = block_rename
    new_boundary = bottom_right
    block = bottom_block
    normal = '1 0 0'
  []
  [bottom_left_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_right_sideset
    new_boundary = bottom_left
    block = bottom_block
    normal = '-1 0 0'
  []
  [bottom_top_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_left_sideset
    new_boundary = bottom_top
    block = bottom_block
    normal = '0 0 1'
  []
  [bottom_bottom_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_top_sideset
    new_boundary = bottom_bottom
    block = bottom_block
    normal = '0  0 -1'
  []
  [bottom_front_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_bottom_sideset
    new_boundary = bottom_front
    block = bottom_block
    normal = '0 1 0'
  []
  [bottom_back_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_front_sideset
    new_boundary = bottom_back
    block = bottom_block
    normal = '0 -1 0'
  []
  [secondary]
    input = bottom_back_sideset
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'top_bottom' # top_back top_left'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'bottom_top'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Variables]
  [disp_x]
    block = '1 2'
  []
  [disp_y]
    block = '1 2'
  []
  [disp_z]
    block = '1 2'
  []
  [lm_x]
    block = 'secondary_lower'
    use_dual = true
  []
  [lm_y]
    block = 'secondary_lower'
    use_dual = true
  []
  [lm_z]
    block = 'secondary_lower'
    use_dual = true
  []
[]

[ICs]
  [disp_z]
    block = 1
    variable = disp_z
    value = '${fparse offset}'
    type = ConstantIC
  []
  [disp_x]
    block = 1
    variable = disp_x
    value = 0
    type = ConstantIC
  []
  [disp_y]
    block = 1
    variable = disp_y
    value = 0
    type = ConstantIC
  []
[]

[Kernels]
  [disp_x]
    type = MatDiffusion
    variable = disp_x
  []
  [disp_y]
    type = MatDiffusion
    variable = disp_y
  []
  [disp_z]
    type = MatDiffusion
    variable = disp_z
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeWeightedGapCartesianLMMechanicalContact
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    lm_x = lm_x
    lm_y = lm_y
    lm_z = lm_z
    variable = lm_x # This can be anything really
    disp_x = disp_x
    disp_y = disp_y
    disp_z = disp_z
    use_displaced_mesh = true
    correct_edge_dropping = true
    c = 1e+02
  []
  [normal_x]
    type = CartesianMortarMechanicalContact
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_x
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
  [normal_y]
    type = CartesianMortarMechanicalContact
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_y
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
  [normal_z]
    type = CartesianMortarMechanicalContact
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_z
    secondary_variable = disp_z
    component = z
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
[]

[BCs]
  [botx]
    type = DirichletBC
    variable = disp_x
    boundary = 'bottom_left bottom_right bottom_front bottom_back'
    value = 0.0
  []
  [boty]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom_left bottom_right bottom_front bottom_back'
    value = 0.0
  []
  [botz]
    type = DirichletBC
    variable = disp_z
    boundary = 'bottom_left bottom_right bottom_front bottom_back'
    value = 0.0
  []
  [topx]
    type = DirichletBC
    variable = disp_x
    boundary = 'top_top'
    value = 0.0
  []
  [topy]
    type = DirichletBC
    variable = disp_y
    boundary = 'top_top'
    value = 0.0
  []
  [topz]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 'top_top'
    function = '-${starting_point} * sin(2 * pi / 40 * t) + ${offset}'
  []
[]

[Preconditioning]
  [vcp]
    type = VCP
    full = true
    lm_variable = 'lm_x lm_y lm_z'
    primary_variable = 'disp_x disp_y disp_z'
    preconditioner = 'LU'
    is_lm_coupling_diagonal = true
    adaptive_condensation = true
  []
[]

[Executioner]
  type = Transient
  end_time = 1
  dt = .5
  dtmin = .01
  solve_type = 'NEWTON'
  petsc_options_iname = '-mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = '1e-5          NONZERO               1e-10'
  l_max_its = 100
  nl_max_its = 30
  # nl_rel_tol = 1e-6
  nl_abs_tol = 1e-12
  line_search = 'none'
  snesmf_reuse_base = false
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  perf_graph = true
  exodus = true
  csv = true
[]

[Postprocessors]
  active = 'num_nl cumulative contact'
  [num_nl]
    type = NumNonlinearIterations
  []
  [cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  []
  [contact]
    type = ContactDOFSetSize
    variable = lm_z
    subdomain = 'secondary_lower'
    execute_on = 'nonlinear timestep_end'
  []
[]

[VectorPostprocessors]
  [contact-pressure]
    type = NodalValueSampler
    block = secondary_lower
    variable = lm_z
    sort_by = 'id'
    execute_on = NONLINEAR
  []
[]

(modules/contact/test/tests/mortar_cartesian_lms/frictionless-weighted-gap-lm.i)

starting_point = 2e-1
offset = 1e-2

[GlobalParams]
  displacements = 'disp_x disp_y'
  diffusivity = 1e0
  scaling = 1e0
[]

[Mesh]
  file = long-bottom-block-1elem-blocks.e
[]

[Variables]
  [disp_x]
    block = '1 2'
  []
  [disp_y]
    block = '1 2'
  []
  [lm_x]
    block = 3
  []
  [lm_y]
    block = 3
  []
[]

[ICs]
  [disp_y]
    block = 2
    variable = disp_y
    value = '${fparse starting_point + offset}'
    type = ConstantIC
  []
[]

[Kernels]
  [disp_x]
    type = MatDiffusion
    variable = disp_x
  []
  [disp_y]
    type = MatDiffusion
    variable = disp_y
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeWeightedGapCartesianLMMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    lm_x = lm_x
    lm_y = lm_y
    variable = lm_x # Shouldn't be needed, but forced by framework
    disp_x = disp_x
    disp_y = disp_y
    use_displaced_mesh = true
    c = 1
  []
  [normal_x]
    type = CartesianMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = lm_x
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [normal_y]
    type = CartesianMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = lm_y
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
[]

[BCs]
  [botx]
    type = DirichletBC
    variable = disp_x
    boundary = 40
    value = 0.0
  []
  [boty]
    type = DirichletBC
    variable = disp_y
    boundary = 40
    value = 0.0
  []
  [topy]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 30
    function = '${starting_point} * cos(2 * pi / 40 * t) + ${offset}'
  []
  [leftx]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 50
    function = '1e-2 * t'
  []
[]

[Executioner]
  type = Transient
  end_time = 200
  dt = 5
  dtmin = 5
  solve_type = 'PJFNK'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -pc_svd_monitor '
                  '-snes_linesearch_monitor'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -mat_mffd_err'
  petsc_options_value = 'lu       NONZERO               1e-15                   1e-5'
  l_max_its = 30
  l_tol = 1e-03
  nl_max_its = 20
  line_search = 'none'
  snesmf_reuse_base = true
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
[]

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

[Postprocessors]
  active = 'num_nl cumulative contact'
  [num_nl]
    type = NumNonlinearIterations
  []
  [cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  []
  [contact]
    type = ContactDOFSetSize
    variable = lm_y
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
[]

(modules/contact/test/tests/mortar_cartesian_lms/two_block_1st_order_constraint_lm_xy.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

theta = 0
velocity = 0.1

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -0.35
    xmax = -0.05
    ymin = -1
    ymax = 0
    nx = 1
    ny = 3
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_sideset_names]
    type = RenameBoundaryGenerator
    input = left_block_sidesets
    old_boundary = '10 11 12 13'
    new_boundary = 'l_bottom l_right l_top l_left'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sideset_names
    subdomain_id = 1
  []
  [right_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.3
    ymin = -1
    ymax = 0
    nx = 1
    ny = 2
    elem_type = QUAD4
  []
  [right_block_sidesets]
    type = RenameBoundaryGenerator
    input = right_block
    old_boundary = '0 1 2 3'
    new_boundary = '20 21 22 23'
  []
  [right_block_sideset_names]
    type = RenameBoundaryGenerator
    input = right_block_sidesets
    old_boundary = '20 21 22 23'
    new_boundary = 'r_bottom r_right r_top r_left'
  []
  [right_block_id]
    type = SubdomainIDGenerator
    input = right_block_sideset_names
    subdomain_id = 2
  []

  [combined_mesh]
    type = MeshCollectionGenerator
    inputs = 'left_block_id right_block_id'
  []

  [left_lower]
    type = LowerDBlockFromSidesetGenerator
    input = combined_mesh
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [right_lower]
    type = LowerDBlockFromSidesetGenerator
    input = left_lower
    sidesets = '23'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []

  [rotate_mesh]
    type = TransformGenerator
    input = right_lower
    transform = ROTATE
    vector_value = '0 0 ${theta}'
  []
[]

[Variables]
  [lm_x]
    block = 'secondary_lower'
    use_dual = true
  []
  [lm_y]
    block = 'secondary_lower'
    use_dual = true
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    incremental = true
    add_variables = true
    block = '1 2'
  []
[]

[Functions]
  [horizontal_movement]
    type = ParsedFunction
    expression = '${velocity} * t * cos(${theta}/180*pi)'
  []
  [vertical_movement]
    type = ParsedFunction
    expression = '${velocity} * t * sin(${theta}/180*pi)'
  []
[]

[BCs]
  [push_left_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 13
    function = horizontal_movement
  []
  [fix_right_x]
    type = DirichletBC
    variable = disp_x
    boundary = 21
    value = 0.0
  []
  [fix_right_y]
    type = DirichletBC
    variable = disp_y
    boundary = 21
    value = 0.0
  []
  [push_left_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 13
    function = vertical_movement
  []
[]

[Materials]
  [elasticity_tensor_left]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 1.0e6
    poissons_ratio = 0.3
  []
  [stress_left]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []

  [elasticity_tensor_right]
    type = ComputeIsotropicElasticityTensor
    block = 2
    youngs_modulus = 1.0e6
    poissons_ratio = 0.3
  []
  [stress_right]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeWeightedGapCartesianLMMechanicalContact
    primary_boundary = '23'
    secondary_boundary = '11'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    lm_x = lm_x
    lm_y = lm_y
    variable = lm_x # This can be anything really
    disp_x = disp_x
    disp_y = disp_y
    use_displaced_mesh = true
    correct_edge_dropping = true
  []
  [normal_x]
    type = CartesianMortarMechanicalContact
    primary_boundary = '23'
    secondary_boundary = '11'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_x
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
  [normal_y]
    type = CartesianMortarMechanicalContact
    primary_boundary = '23'
    secondary_boundary = '11'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_y
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu        superlu_dist                  NONZERO               1e-10'

  line_search = none

  dt = 0.1
  dtmin = 0.1
  end_time = 1.0

  l_max_its = 100

  nl_max_its = 20
  nl_rel_tol = 1e-6
  snesmf_reuse_base = false
[]

[Outputs]
  exodus = false
  file_base = './output/1st_order_${theta}_degree_out'
  [comp]
    type = CSV
    show = 'tot_lin_it tot_nonlin_it'
    execute_on = 'FINAL'
  []
[]

[Postprocessors]
  [avg_disp_x]
    type = ElementAverageValue
    variable = disp_x
    block = '1 2'
  []
  [avg_disp_y]
    type = ElementAverageValue
    variable = disp_y
    block = '1 2'
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
    block = '1 2'
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
    block = '1 2'
  []
  [min_disp_x]
    type = ElementExtremeValue
    variable = disp_x
    block = '1 2'
    value_type = min
  []
  [min_disp_y]
    type = ElementExtremeValue
    variable = disp_y
    block = '1 2'
    value_type = min
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
[]

(modules/contact/test/tests/mortar_aux_kernels/pressure-aux-frictionless-3d.i)

starting_point = 0.25
offset = 0.00

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  diffusivity = 1e0
  scaling = 1e0
[]

[Problem]
  # error_on_jacobian_nonzero_reallocation = true
[]

[Mesh]
  second_order = false
  [top_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 3
    nz = 3
    xmin = -0.25
    xmax = 0.25
    ymin = -0.25
    ymax = 0.25
    zmin = -0.25
    zmax = 0.25
    elem_type = HEX8
  []
  [rotate_top_block]
    type = TransformGenerator
    input = top_block
    transform = ROTATE
    vector_value = '0 0 0'
  []
  [top_block_sidesets]
    type = RenameBoundaryGenerator
    input = rotate_top_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = 'top_bottom top_back top_right top_front top_left top_top'
  []
  [top_block_id]
    type = SubdomainIDGenerator
    input = top_block_sidesets
    subdomain_id = 1
  []
  [bottom_block]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 10
    nz = 2
    xmin = -.5
    xmax = .5
    ymin = -.5
    ymax = .5
    zmin = -.3
    zmax = -.25
    elem_type = HEX8
  []
  [bottom_block_id]
    type = SubdomainIDGenerator
    input = bottom_block
    subdomain_id = 2
  []
  [bottom_block_change_boundary_id]
    type = RenameBoundaryGenerator
    input = bottom_block_id
    old_boundary = '0 1 2 3 4 5'
    new_boundary = '100 101 102 103 104 105'
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'top_block_id bottom_block_change_boundary_id'
  []
  [block_rename]
    type = RenameBlockGenerator
    input = combined
    old_block = '1 2'
    new_block = 'top_block bottom_block'
  []
  [bottom_right_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = block_rename
    new_boundary = bottom_right
    block = bottom_block
    normal = '1 0 0'
  []
  [bottom_left_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_right_sideset
    new_boundary = bottom_left
    block = bottom_block
    normal = '-1 0 0'
  []
  [bottom_top_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_left_sideset
    new_boundary = bottom_top
    block = bottom_block
    normal = '0 0 1'
  []
  [bottom_bottom_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_top_sideset
    new_boundary = bottom_bottom
    block = bottom_block
    normal = '0  0 -1'
  []
  [bottom_front_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_bottom_sideset
    new_boundary = bottom_front
    block = bottom_block
    normal = '0 1 0'
  []
  [bottom_back_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = bottom_front_sideset
    new_boundary = bottom_back
    block = bottom_block
    normal = '0 -1 0'
  []
  [secondary]
    input = bottom_back_sideset
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'top_bottom' # top_back top_left'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'bottom_top'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Variables]
  [disp_x]
    block = '1 2'
  []
  [disp_y]
    block = '1 2'
  []
  [disp_z]
    block = '1 2'
  []
  [lm_x]
    block = 'secondary_lower'
    use_dual = true
  []
  [lm_y]
    block = 'secondary_lower'
    use_dual = true
  []
  [lm_z]
    block = 'secondary_lower'
    use_dual = true
  []
[]

[AuxVariables]
  [normal_lm]
    family = LAGRANGE
    order = FIRST
  []
[]

[AuxKernels]
  [normal_lm]
    type = MortarPressureComponentAux
    variable = normal_lm
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    lm_var_x = lm_x
    lm_var_y = lm_y
    lm_var_z = lm_z
    component = 'NORMAL'
    boundary = 'top_bottom'
  []
[]

[ICs]
  [disp_z]
    block = 1
    variable = disp_z
    value = '${fparse offset}'
    type = ConstantIC
  []
  [disp_x]
    block = 1
    variable = disp_x
    value = 0
    type = ConstantIC
  []
  [disp_y]
    block = 1
    variable = disp_y
    value = 0
    type = ConstantIC
  []
[]

[Kernels]
  [disp_x]
    type = MatDiffusion
    variable = disp_x
  []
  [disp_y]
    type = MatDiffusion
    variable = disp_y
  []
  [disp_z]
    type = MatDiffusion
    variable = disp_z
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeWeightedGapCartesianLMMechanicalContact
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    lm_x = lm_x
    lm_y = lm_y
    lm_z = lm_z
    variable = lm_x # This can be anything really
    disp_x = disp_x
    disp_y = disp_y
    disp_z = disp_z
    use_displaced_mesh = true
    correct_edge_dropping = true
    c = 1e+02
  []
  [normal_x]
    type = CartesianMortarMechanicalContact
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_x
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
  [normal_y]
    type = CartesianMortarMechanicalContact
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_y
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
  [normal_z]
    type = CartesianMortarMechanicalContact
    primary_boundary = 'bottom_top'
    secondary_boundary = 'top_bottom'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_z
    secondary_variable = disp_z
    component = z
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
[]

[BCs]
  [botx]
    type = DirichletBC
    variable = disp_x
    boundary = 'bottom_left bottom_right bottom_front bottom_back'
    value = 0.0
  []
  [boty]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom_left bottom_right bottom_front bottom_back'
    value = 0.0
  []
  [botz]
    type = DirichletBC
    variable = disp_z
    boundary = 'bottom_left bottom_right bottom_front bottom_back'
    value = 0.0
  []
  [topx]
    type = DirichletBC
    variable = disp_x
    boundary = 'top_top'
    value = 0.0
  []
  [topy]
    type = DirichletBC
    variable = disp_y
    boundary = 'top_top'
    value = 0.0
  []
  [topz]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 'top_top'
    function = '-${starting_point} * sin(2 * pi / 40 * t) + ${offset}'
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type '
                        '-pc_factor_shift_amount'
  petsc_options_value = 'lu superlu_dist 1e-5          NONZERO               1e-10'
  end_time = 1
  dt = .5
  dtmin = .01
  l_max_its = 100
  nl_max_its = 30
  # nl_rel_tol = 1e-6
  nl_abs_tol = 1e-12
  line_search = 'none'
  snesmf_reuse_base = false
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = false
  csv = true
  execute_on = 'FINAL'
[]

[VectorPostprocessors]
  [normal_lm]
    type = NodalValueSampler
    block = secondary_lower
    variable = normal_lm
    sort_by = 'id'
  []
[]

(modules/contact/test/tests/mortar_aux_kernels/pressure-aux-frictionless.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -0.35
    xmax = -0.05
    ymin = -1
    ymax = 0
    nx = 1
    ny = 3
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_sideset_names]
    type = RenameBoundaryGenerator
    input = left_block_sidesets
    old_boundary = '10 11 12 13'
    new_boundary = 'l_bottom l_right l_top l_left'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sideset_names
    subdomain_id = 1
  []
  [right_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.3
    ymin = -1
    ymax = 0
    nx = 1
    ny = 2
    elem_type = QUAD4
  []
  [right_block_sidesets]
    type = RenameBoundaryGenerator
    input = right_block
    old_boundary = '0 1 2 3'
    new_boundary = '20 21 22 23'
  []
  [right_block_sideset_names]
    type = RenameBoundaryGenerator
    input = right_block_sidesets
    old_boundary = '20 21 22 23'
    new_boundary = 'r_bottom r_right r_top r_left'
  []
  [right_block_id]
    type = SubdomainIDGenerator
    input = right_block_sideset_names
    subdomain_id = 2
  []

  [combined_mesh]
    type = MeshCollectionGenerator
    inputs = 'left_block_id right_block_id'
  []

  [left_lower]
    type = LowerDBlockFromSidesetGenerator
    input = combined_mesh
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [right_lower]
    type = LowerDBlockFromSidesetGenerator
    input = left_lower
    sidesets = '23'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []

  uniform_refine = 1
[]

[Variables]
  [lm_x]
    block = 'secondary_lower'
    use_dual = true
  []
  [lm_y]
    block = 'secondary_lower'
    use_dual = true
  []
[]

[AuxVariables]
  [normal_lm]
    family = LAGRANGE
    order = FIRST
  []
[]

[AuxKernels]
  [normal_lm]
    type = MortarPressureComponentAux
    variable = normal_lm
    primary_boundary = '23'
    secondary_boundary = '11'
    lm_var_x = lm_x
    lm_var_y = lm_y
    component = 'NORMAL'
    boundary = '11'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    incremental = true
    add_variables = true
    block = '1 2'
  []
[]

[Functions]
  [horizontal_movement]
    type = ParsedFunction
    expression = '0.1 * t'
  []
  [vertical_movement]
    type = ConstantFunction
    value = '0.0'
  []
[]

[BCs]
  [push_left_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 13
    function = horizontal_movement
  []
  [fix_right_x]
    type = DirichletBC
    variable = disp_x
    boundary = 21
    value = 0.0
  []
  [fix_right_y]
    type = DirichletBC
    variable = disp_y
    boundary = 21
    value = 0.0
  []
  [push_left_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 13
    function = vertical_movement
  []
[]

[Materials]
  [elasticity_tensor_left]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 1.0e6
    poissons_ratio = 0.3
  []
  [stress_left]
    type = ComputeFiniteStrainElasticStress
    block = 1
  []

  [elasticity_tensor_right]
    type = ComputeIsotropicElasticityTensor
    block = 2
    youngs_modulus = 1.0e6
    poissons_ratio = 0.3
  []
  [stress_right]
    type = ComputeFiniteStrainElasticStress
    block = 2
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeWeightedGapCartesianLMMechanicalContact
    primary_boundary = '23'
    secondary_boundary = '11'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    lm_x = lm_x
    lm_y = lm_y
    variable = lm_x # This can be anything really
    disp_x = disp_x
    disp_y = disp_y
    use_displaced_mesh = true
    correct_edge_dropping = true
    interpolate_normals = false
  []
  [normal_x]
    type = CartesianMortarMechanicalContact
    primary_boundary = '23'
    secondary_boundary = '11'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_x
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
  [normal_y]
    type = CartesianMortarMechanicalContact
    primary_boundary = '23'
    secondary_boundary = '11'
    primary_subdomain = 'primary_lower'
    secondary_subdomain = 'secondary_lower'
    variable = lm_y
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    correct_edge_dropping = true
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type '
                        '-pc_factor_shift_amount'
  petsc_options_value = 'lu superlu_dist 1e-5          NONZERO               1e-10'

  line_search = none

  dt = 0.1
  dtmin = 0.1
  end_time = 1.0

  l_max_its = 100

  nl_max_its = 20
  nl_rel_tol = 1e-6
  snesmf_reuse_base = false
[]

[Outputs]
  exodus = false
  csv = true
  execute_on = 'FINAL'
[]

[VectorPostprocessors]
  [normal_lm]
    type = NodalValueSampler
    block = 'secondary_lower'
    variable = normal_lm
    sort_by = 'id'
  []
[]

(modules/contact/include/constraints/ComputeFrictionalForceCartesianLMMechanicalContact.h)

// This file is part of the MOOSE framework
// https://www.mooseframework.org
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "ComputeWeightedGapCartesianLMMechanicalContact.h"

#include <unordered_map>

/**
 * Computes the weighted gap that will later be used to enforce the
 * zero-penetration mechanical contact conditions
 */
class ComputeFrictionalForceCartesianLMMechanicalContact
  : public ComputeWeightedGapCartesianLMMechanicalContact
{
public:
  static InputParameters validParams();

  ComputeFrictionalForceCartesianLMMechanicalContact(const InputParameters & parameters);

  void residualSetup() override;
  void post() override;

  /**
   * Copy of the post routine but that skips assembling inactive nodes
   */
  void
  incorrectEdgeDroppingPost(const std::unordered_set<const Node *> & inactive_lm_nodes) override;

protected:
  /**
   * Computes properties that are functions only of the current quadrature point (\p _qp), e.g.
   * indepedent of shape functions
   */
  virtual void computeQpProperties() override;

  /**
   * Computes properties that are functions both of \p _qp and \p _i, for example the weighted gap
   */
  virtual void computeQpIProperties() override;

  /**
   * Method called from \p post(). Used to enforce node-associated constraints. E.g. for the base \p
   * ComputeWeightedGapLMMechanicalContact we enforce the zero-penetration constraint in this method
   * using an NCP function. This is also where we actually feed the node-based constraint
   * information into the system residual and Jacobian
   */
  virtual void enforceConstraintOnDof(const DofObject * const dof) override;

  /// A map from node to two weighted tangential velocities
  std::unordered_map<const DofObject *, std::array<ADReal, 2>> _dof_to_weighted_tangential_velocity;

  /// An array of two pointers to avoid copies
  std::array<const ADReal *, 2> _tangential_vel_ptr = {{nullptr, nullptr}};

  /// The value of the tangential velocity vectors at the current node
  ADRealVectorValue _qp_tangential_velocity_nodal;

  /// Numerical factor used in the tangential constraints for convergence purposes
  const Real _c_t;

  /// x-velocity on the secondary face
  const ADVariableValue & _secondary_x_dot;

  /// x-velocity on the primary face
  const ADVariableValue & _primary_x_dot;

  /// y-velocity on the secondary face
  const ADVariableValue & _secondary_y_dot;

  /// y-velocity on the primary face
  const ADVariableValue & _primary_y_dot;

  /// z-velocity on the secondary face
  const ADVariableValue * const _secondary_z_dot;

  /// z-velocity on the primary face
  const ADVariableValue * const _primary_z_dot;

  /// Friction coefficient
  const Real _mu;

  /// Small contact pressure value to trigger computation of frictional forces
  const Real _epsilon;
};

Input Parameters
Input Files
Child Objects
References