ComputeDynamicWeightedGapLMMechanicalContact

Computes the normal contact mortar constraints for dynamic simulations

This object is virtually analogous to ComputeWeightedGapLMMechanicalContact, but it is used for dynamic simulations.

When the mortar mechanical contact constraints are used in dynamic simulations, the normal contact constraints need to be stabilized by ensuring that the normal gap time derivative is included to guarantee a dynamic contact. This is a means of guaranteeing the 'persistency' condition, i.e. not only do we enforce the constraints instantaneously, but also that the contact interface will remain in contact locally. This approximate contact constraint stabilization is performed in ComputeDynamicWeightedGapLMMechanicalContact. Once nodal contact is established, the constraint enforcement is switched to the persistency equation:

$var element = document.getElementById("moose-equation-8d60ba3c-d52a-4740-8d7e-763e6b133a5d");katex.render("\\begin{aligned} (\\tilde{g}_n)_j \\coloneqq \\dot{\\tilde{g}}_{nj} \\cdot \\Delta t \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-3ef9dca1-58c9-42e5-92b5-1870306c2a74");katex.render("\\,\\dot{}\\,", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denotes the first time derivative, $var element = document.getElementById("moose-equation-ff2d92a0-3346-4f82-aed2-b7d2d50571a8");katex.render("\\Delta t", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the time step increment, $var element = document.getElementById("moose-equation-7be09d61-7fad-44a3-bba0-b9e7b26a9342");katex.render("j", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ refers to an arbitrary node.

The capture_tolerance is an optional contact parameter used in dynamic contact constraints to determine when to impose the persistency condition for normal contact.

For relevant, general equations, see (Tal and Hager, 2018). Also, for discussion on the relevance of normal contact constraint stabilization for energy conservation and contact force accuracy, in the context of mortar constraints, see (Recuero and Lindsay, 2022).

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
newmark_betaBeta parameter for the Newmark time integrator
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Beta parameter for the Newmark time integrator
newmark_gammaGamma parameter for the Newmark time integrator
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Gamma parameter for the Newmark time integrator
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
capture_tolerance1e-05Parameter describing a gap threshold for the application of the persistency constraint in dynamic simulations.
Default:1e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Parameter describing a gap threshold for the application of the persistency constraint in dynamic simulations.
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
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
wear_depthThe name of the mortar auxiliary variable that is used to modify the weighted gap definition
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of the mortar auxiliary variable that is used to modify the weighted gap definition

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_aux_kernels/block-dynamics-aux-vel.i)
(modules/contact/test/tests/mortar_aux_kernels/block-dynamics-aux-wear.i)
(modules/contact/test/tests/mortar_dynamics/block-dynamics.i)
(modules/contact/test/tests/mortar_dynamics/block-dynamics-reference.i)

Child Objects

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

References

Antonio Recuero and Alexander Lindsay. On practical aspects of variational consistency in contact dynamics. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, volume 86304, V009T09A003. American Society of Mechanical Engineers, 2022.

@inproceedings{recuero2022practical,
    author = "Recuero, Antonio and Lindsay, Alexander",
    title = "On Practical Aspects of Variational Consistency in Contact Dynamics",
    booktitle = "International Design Engineering Technical Conferences and Computers and Information in Engineering Conference",
    volume = "86304",
    pages = "V009T09A003",
    year = "2022",
    organization = "American Society of Mechanical Engineers"
}

Yuval Tal and Bradford H Hager. Dynamic mortar finite element method for modeling of shear rupture on frictional rough surfaces. Computational Mechanics, 61(6):699–716, 2018.

@article{tal2018dynamic,
    author = "Tal, Yuval and Hager, Bradford H",
    title = "Dynamic mortar finite element method for modeling of shear rupture on frictional rough surfaces",
    journal = "Computational Mechanics",
    volume = "61",
    number = "6",
    pages = "699--716",
    year = "2018",
    publisher = "Springer"
}

(modules/contact/test/tests/mortar_aux_kernels/block-dynamics-aux-vel.i)

starting_point = 2e-1
offset = -0.19

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

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

[Variables]
  [disp_x]
    block = '1 2'
  []
  [disp_y]
    block = '1 2'
  []
  [normal_lm]
    block = 3
    use_dual = true
  []
[]

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

[Kernels]
  [DynamicTensorMechanics]
    displacements = 'disp_x disp_y'
    generate_output = 'stress_xx stress_yy'
    strain = FINITE
    block = '1 2'
    zeta = 1.0
    alpha = 0.0
  []
  [inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    beta = 0.25
    gamma = 0.5
    alpha = 0
    eta = 0.0
    block = '1 2'
  []
  [inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    beta = 0.25
    gamma = 0.5
    alpha = 0
    eta = 0.0
    block = '1 2'
  []
[]

[Materials]
  [elasticity_2]
    type = ComputeIsotropicElasticityTensor
    block = '2'
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  []
  [elasticity_1]
    type = ComputeIsotropicElasticityTensor
    block = '1'
    youngs_modulus = 1e8
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [strain]
    type = ComputeFiniteStrain
    block = '1 2'
  []
  [density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '7750'
  []
[]

[AuxVariables]
  [gap_vel]
    block = '3'
  []
  [vel_x]
    block = '1 2'
  []
  [accel_x]
    block = '1 2'
  []
  [vel_y]
    block = '1 2'
  []
  [accel_y]
    block = '1 2'
  []
  [vel_z]
    block = '1 2'
  []
  [accel_z]
    block = '1 2'
  []
[]

[AuxKernels]
  [gap_vel]
    type = WeightedGapVelAux
    variable = gap_vel
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    disp_x = disp_x
    disp_y = disp_y
    correct_edge_dropping = true
    execute_on = 'TIMESTEP_END'
  []
  [accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = 'linear timestep_end'
  []
  [vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = 'linear timestep_end'
  []
  [accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = 'linear timestep_end'
  []
  [vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = 'linear timestep_end'
  []
[]

[UserObjects]
  [weighted_gap_uo]
    type = LMWeightedGapUserObject
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    lm_variable = normal_lm
    disp_x = disp_x
    disp_y = disp_y
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeDynamicWeightedGapLMMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    disp_x = disp_x
    disp_y = disp_y
    use_displaced_mesh = true
    c = 1e4
    capture_tolerance = 1.0e-5
    newmark_beta = 0.25
    newmark_gamma = 0.5
  []
  [normal_x]
    type = NormalMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
[]

[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 / 4 * t) + ${offset}'
  []
  [leftx]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 50
    function = '1e-2 * t'
  []
[]

[Executioner]
  type = Transient
  end_time = 0.1
  dt = 0.05
  dtmin = 0.05
  solve_type = 'PJFNK'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -pc_svd_monitor '
                  '-snes_linesearch_monitor -snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type -pc_factor_shift_type -pc_factor_shift_amount -mat_mffd_err '
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15                   1e-5'
  nl_max_its = 20
  line_search = 'none'
  snesmf_reuse_base = false

  [TimeIntegrator]
    type = NewmarkBeta
    beta = 0.25
    gamma = 0.5
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
  checkpoint = 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 = normal_lm
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
[]

(modules/contact/test/tests/mortar_aux_kernels/block-dynamics-aux-wear.i)

starting_point = 0.5e-1
offset = -0.05

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

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

[Variables]
  [disp_x]
    block = '1 2'
  []
  [disp_y]
    block = '1 2'
  []
  [normal_lm]
    block = 3
    use_dual = true
  []
[]

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

[Kernels]
  [DynamicTensorMechanics]
    displacements = 'disp_x disp_y'
    generate_output = 'stress_xx stress_yy'
    strain = FINITE
    block = '1 2'
    zeta = 1.0
    hht_alpha = 0.0
  []
  [inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    beta = 0.25
    gamma = 0.5
    alpha = 0
    eta = 0.0
    block = '1 2'
  []
  [inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    beta = 0.25
    gamma = 0.5
    alpha = 0
    eta = 0.0
    block = '1 2'
  []
[]

[Materials]
  [elasticity_2]
    type = ComputeIsotropicElasticityTensor
    block = '2'
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  []
  [elasticity_1]
    type = ComputeIsotropicElasticityTensor
    block = '1'
    youngs_modulus = 1e8
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [strain]
    type = ComputeFiniteStrain
    block = '1 2'
  []
  [density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '7750'
  []
[]

[AuxVariables]
  [worn_depth]
    block = '3'
  []
  [vel_x]
    block = '1 2'
  []
  [accel_x]
    block = '1 2'
  []
  [vel_y]
    block = '1 2'
  []
  [accel_y]
    block = '1 2'
  []
  [vel_z]
    block = '1 2'
  []
  [accel_z]
    block = '1 2'
  []
[]

[AuxKernels]
  [worn_depth]
    type = MortarArchardsLawAux
    variable = worn_depth
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    displacements = 'disp_x disp_y'
    friction_coefficient = 0.5
    energy_wear_coefficient = 1.0
    normal_pressure = normal_lm
  []
  [accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = 'linear timestep_end'
  []
  [vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = 'linear timestep_end'
  []
  [accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = 'linear timestep_end'
  []
  [vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = 'linear timestep_end'
  []
[]

[UserObjects]
  [weighted_gap_uo]
    type = LMWeightedGapUserObject
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    lm_variable = normal_lm
    disp_x = disp_x
    disp_y = disp_y
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeDynamicWeightedGapLMMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    disp_x = disp_x
    disp_y = disp_y
    use_displaced_mesh = true
    c = 1e4
    capture_tolerance = 1.0e-5
    newmark_beta = 0.25
    newmark_gamma = 0.5
  []
  [normal_x]
    type = NormalMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
[]

[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(8.0 * pi / 4 * t) + ${offset}'
  []
  [leftx]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 50
    function = '1e-2 * t'
  []
[]

[Executioner]
  type = Transient
  end_time = 0.675
  dt = 0.075
  dtmin = .075
  solve_type = 'NEWTON'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -pc_svd_monitor '
                  '-snes_linesearch_monitor -snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type -pc_factor_shift_type -pc_factor_shift_amount '
  petsc_options_value = 'lu       superlu_dist                  NONZERO               1e-15'
  nl_max_its = 30
  line_search = 'l2'
  snesmf_reuse_base = false

  [TimeIntegrator]
    type = NewmarkBeta
    beta = 0.25
    gamma = 0.5
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
  checkpoint = 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 = normal_lm
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
[]

(modules/contact/test/tests/mortar_dynamics/block-dynamics.i)

starting_point = 2e-1
offset = -0.19

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

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

[Variables]
  [disp_x]
    block = '1 2'
  []
  [disp_y]
    block = '1 2'
  []
  [normal_lm]
    block = 3
    use_dual = true
  []
[]

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

[Kernels]
  [DynamicTensorMechanics]
    displacements = 'disp_x disp_y'
    generate_output = 'stress_xx stress_yy'
    strain = FINITE
    block = '1 2'
    zeta = 1.0
    alpha = 0.0
  []
  [inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    beta = 0.25
    gamma = 0.5
    alpha = 0
    eta = 0.0
    block = '1 2'
  []
  [inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    beta = 0.25
    gamma = 0.5
    alpha = 0
    eta = 0.0
    block = '1 2'
  []
[]

[Materials]
  [elasticity_2]
    type = ComputeIsotropicElasticityTensor
    block = '2'
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  []
  [elasticity_1]
    type = ComputeIsotropicElasticityTensor
    block = '1'
    youngs_modulus = 1e8
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [strain]
    type = ComputeFiniteStrain
    block = '1 2'
  []
  [density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '7750'
  []
[]

[AuxVariables]
  [vel_x]
    block = '1 2'
  []
  [accel_x]
    block = '1 2'
  []
  [vel_y]
    block = '1 2'
  []
  [accel_y]
    block = '1 2'
  []
  [vel_z]
    block = '1 2'
  []
  [accel_z]
    block = '1 2'
  []
[]

[AuxKernels]
  [accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = 'LINEAR timestep_end'
  []
  [vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = 'LINEAR timestep_end'
  []
  [accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = 'LINEAR timestep_end'
  []
  [vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = 'LINEAR timestep_end'
  []
[]

# User object provides the contact force (e.g. LM)
# for the application of the generalized force
[UserObjects]
  [weighted_gap_uo]
    type = LMWeightedGapUserObject
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    lm_variable = normal_lm
    disp_x = disp_x
    disp_y = disp_y
  []
[]

[Constraints]
  [weighted_gap_lm]
    type = ComputeDynamicWeightedGapLMMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    disp_x = disp_x
    disp_y = disp_y
    use_displaced_mesh = true
    c = 1e4
    capture_tolerance = 1.0e-5
    newmark_beta = 0.25
    newmark_gamma = 0.5
  []
  [normal_x]
    type = NormalMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
[]

[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 / 4 * t) + ${offset}'
  []
  [leftx]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 50
    function = '1e-2 * t'
  []
[]

[Executioner]
  type = Transient
  end_time = 75
  dt = 0.05
  dtmin = .05
  solve_type = 'PJFNK'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -pc_svd_monitor '
                  '-snes_linesearch_monitor -snes_ksp_ew'
  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'
  nl_max_its = 20
  line_search = 'none'
  snesmf_reuse_base = false

  [TimeIntegrator]
    type = NewmarkBeta
    beta = 0.25
    gamma = 0.5
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
  checkpoint = 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 = normal_lm
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
[]

(modules/contact/test/tests/mortar_dynamics/block-dynamics-reference.i)

starting_point = 2e-1
offset = -0.19

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

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

[Variables]
  [disp_x]
    block = '1 2'
  []
  [disp_y]
    block = '1 2'
  []
  [normal_lm]
    block = 3
    use_dual = true
  []
[]

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

[Kernels]
  [DynamicTensorMechanics]
    displacements = 'disp_x disp_y'
    generate_output = 'stress_xx stress_yy'
    strain = FINITE
    block = '1 2'
    zeta = 1.0
    alpha = 0.0
  []
  [inertia_x]
    type = InertialForce
    variable = disp_x
    velocity = vel_x
    acceleration = accel_x
    beta = 0.25
    gamma = 0.5
    alpha = 0
    eta = 0.0
    block = '1 2'
  []
  [inertia_y]
    type = InertialForce
    variable = disp_y
    velocity = vel_y
    acceleration = accel_y
    beta = 0.25
    gamma = 0.5
    alpha = 0
    eta = 0.0
    block = '1 2'
  []
[]

[Materials]
  [elasticity_2]
    type = ComputeIsotropicElasticityTensor
    block = '2'
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  []
  [elasticity_1]
    type = ComputeIsotropicElasticityTensor
    block = '1'
    youngs_modulus = 1e8
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [strain]
    type = ComputeFiniteStrain
    block = '1 2'
  []
  [density]
    type = GenericConstantMaterial
    block = '1 2'
    prop_names = 'density'
    prop_values = '7750'
  []
[]

[AuxVariables]
  [vel_x]
    block = '1 2'
  []
  [accel_x]
    block = '1 2'
  []
  [vel_y]
    block = '1 2'
  []
  [accel_y]
    block = '1 2'
  []
  [vel_z]
    block = '1 2'
  []
  [accel_z]
    block = '1 2'
  []
  [kinetic_energy]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_energy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [accel_x]
    type = NewmarkAccelAux
    variable = accel_x
    displacement = disp_x
    velocity = vel_x
    beta = 0.25
    execute_on = 'timestep_end'
  []
  [vel_x]
    type = NewmarkVelAux
    variable = vel_x
    acceleration = accel_x
    gamma = 0.5
    execute_on = 'timestep_end'
  []
  [accel_y]
    type = NewmarkAccelAux
    variable = accel_y
    displacement = disp_y
    velocity = vel_y
    beta = 0.25
    execute_on = 'timestep_end'
  []
  [vel_y]
    type = NewmarkVelAux
    variable = vel_y
    acceleration = accel_y
    gamma = 0.5
    execute_on = 'timestep_end'
  []
  [kinetic_energy]
    type = KineticEnergyAux
    block = '1 2'
    variable = kinetic_energy
    newmark_velocity_x = vel_x
    newmark_velocity_y = vel_y
    newmark_velocity_z = 0.0
    density = density
  []
  [elastic_energy]
    type = ElasticEnergyAux
    variable = elastic_energy
    block = '1 2'
  []
[]


# User object provides the contact force (e.g. LM)
# for the application of the generalized force
[UserObjects]
  [weighted_gap_uo]
    type = LMWeightedGapUserObject
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    lm_variable = normal_lm
    disp_x = disp_x
    disp_y = disp_y
  []
[]


[Constraints]
  # Not using 'dynamic' constraints results in poor enforcement of contact
  # constraints and lack of kinetic and elastic energy conservation.
  [weighted_gap_lm]
    type = ComputeDynamicWeightedGapLMMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    disp_x = disp_x
    disp_y = disp_y
    newmark_beta = 0.25
    newmark_gamma = 0.5
    use_displaced_mesh = true
    # Capture tolerance is important. If too small, stabilization takes longer
    capture_tolerance = 1.0e-5
    c = 1.0e6
  []

  [normal_x]
    type = NormalMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    primary_boundary = 20
    secondary_boundary = 10
    primary_subdomain = 4
    secondary_subdomain = 3
    variable = normal_lm
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = weighted_gap_uo
  []
[]

[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 / 4 * t) + ${offset}'
  []
  [leftx]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 30 # 50
    function = '0' # '1e-2*t'
  []
[]

[Executioner]
  type = Transient
  end_time = 0.275 # 8.0
  dt = 0.025
  dtmin = .025
  solve_type = 'NEWTON'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_linesearch_monitor'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       NONZERO               1e-15'
  nl_max_its = 50
  line_search = 'none'
  [TimeIntegrator]
    type = NewmarkBeta
    beta = 0.25
    gamma = 0.5
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
  checkpoint = true
  csv = true
[]

[Postprocessors]
  active = 'contact total_kinetic_energy total_elastic_energy'
  [num_nl]
    type = NumNonlinearIterations
  []
  [cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  []
  [contact]
    type = ContactDOFSetSize
    variable = normal_lm
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
  [total_kinetic_energy]
    type = ElementIntegralVariablePostprocessor
    variable = kinetic_energy
    block = '1 2'
  []
  [total_elastic_energy]
    type = ElementIntegralVariablePostprocessor
    variable = elastic_energy
    block = '1 2'
  []
[]

(modules/contact/include/constraints/ComputeDynamicFrictionalForceLMMechanicalContact.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 "ComputeDynamicWeightedGapLMMechanicalContact.h"

/**
 * Computes the mortar tangential frictional forces for dynamic simulations.
 */
class ComputeDynamicFrictionalForceLMMechanicalContact
  : public ComputeDynamicWeightedGapLMMechanicalContact
{
public:
  static InputParameters validParams();

  ComputeDynamicFrictionalForceLMMechanicalContact(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
   * ComputeFrictionalForceLMMechanicalContact we enforce PDASS frictional constraints. 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;

  /**
   * Method called from \p post(). Used to enforce node-associated constraints. E.g. for the base \p
   * ComputeFrictionalForceLMMechanicalContact we enforce PDASS frictional constraints. This is also
   * where we actually feed the node-based constraint information into the system residual and
   * Jacobian. Method used to enforce frictional constraints in three-dimensional simulations.
   */
  virtual void enforceConstraintOnDof3d(const DofObject * const dof);

  void timestepSetup() override;

  /**
   * Apply constant or function-based friction coefficient
   */
  ADReal computeFrictionValue(const ADReal & contact_pressure,
                              const Real & tangential_vel,
                              const Real & tangential_vel_dir);

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

  /// A map from node to two tangential velocities. Required to have direct connection to physics.
  std::unordered_map<const DofObject *, std::array<Real, 2>> _dof_to_real_tangential_velocity;

  /// A map from node to two old tangential velocities. Required to have direct connection to physics.
  std::unordered_map<const DofObject *, std::array<Real, 2>> _dof_to_old_real_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;

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

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

  /// Frictional Lagrange's multiplier variable pointers
  std::vector<MooseVariable *> _friction_vars;

  /// 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;

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

  /// Friction coefficient
  const Real _mu;

  /// input function
  const Function * const _function_friction;

  /// Boolean to determine whether the friction coefficient is taken from a function
  const bool _has_friction_function;

  /// Automatic flag to determine whether we are doing three-dimensional work
  bool _3d;
};

Input Parameters
Input Files
Child Objects
References