ADRebarBondSlipConstraint / RebarBondSlipConstraint

Constraint using a physical model to enforce the bond-slip behavior between concrete and rebar.

ADRebarBondSlipConstraint implements a node-to-element constraint designed to apply the bond-slip relations between concrete and reinforcement bars. The rebar node is always "secondary" with the concrete element being the "primary". It uses a bond-slip model that assigns bond stress based on the slip values calculated as the relative displacement between concrete and rebar.

The ADRebarBondSlipConstraint is recommended as the nonAD version, RebarBondSlipConstraint, as currently implemented does not have an exact Jacobian, potentially leading to convergence issues that can be be resolved by using the ADRebarBondSlipConstraint. There is also very little overhead or input file syntax change required for using ADRebarBondSlipConstraint as the AD terms are limited to the constraint blocks as shown in Listing 1.

warning:ADRebarBondSlipConstraint only works for PENALTY formulation

EqualValueEmbeddedConstraint / ADEqualValueEmbeddedConstraint provides an explaination on why KINEMATIC formulation does not work.

Two bond-slip models have been implemented. The default model selected by "bondslip_model"=concrete_rebar_model is the nonlinear model from Mehlhorn et al. (1985) fit to experimental concrete rebar data and given as

$var element = document.getElementById("moose-equation-17017af7-1590-4493-90e1-28b0148c7eb0");katex.render(" \\sigma_s = \\begin{cases} \\sigma_{max} \\left[ 0.5 \\left(\\frac{\\Delta}{\\Delta_T}\\right) - 4.5 \\left(\\frac{\\Delta}{\\Delta_T}\\right)^2 + 1.4 \\left(\\frac{\\Delta}{\\Delta_T}\\right)^3 \\right] & \\Delta < \\Delta_T \\\\ 1.9 \\sigma_{max} & \\Delta \\geq \\Delta_T \\end{cases}", element, {displayMode:true,throwOnError:false});$

where, $var element = document.getElementById("moose-equation-a5fce9c3-6cbe-4f59-940f-1df86bd53e4e");katex.render("\\sigma_s", element, {displayMode:false,throwOnError:false});$ is the bond stress, $var element = document.getElementById("moose-equation-fe7404fa-d660-48bb-bbb3-b12a0531d6e2");katex.render("\\sigma_{max}", element, {displayMode:false,throwOnError:false});$ is the "max_bond_stress" related to the compressive strength of the concrete, $var element = document.getElementById("moose-equation-376fdbe4-0ac3-480f-bee4-efcde5107751");katex.render("\\Delta", element, {displayMode:false,throwOnError:false});$ is the slip calculated as the relative displacement between the concrete and rebar in the axial direction of the rebar, and $var element = document.getElementById("moose-equation-170376cf-1eba-47c1-968c-f8fd69aead36");katex.render("\\Delta_T", element, {displayMode:false,throwOnError:false});$ is the "transitional_slip_value" at which the maximum bond stress is reached. The "rebar_radius" is also required by this model to convert the bond stress to a constraint force.

The second bond-slip model is an elastic perfect plastic version of the nonlinear model. The initial slip of the rebar-concrete bond is a linear function of stress. Linear slip continues up to "max_bond_stress" and "transitional_slip_value". After max_bond_stress is reached, additional slip occurs at a constant force. Unloading follows the slope of the linear loading curve. This model is selected by "bondslip_model"=elastic_perfect_plastic_model.

Information on the bond-slip model's behavior can be written to AuxVariable through the "output_axial_slip", "output_axial_force", and "output_axial_plastic_slip" parameters. "output_axial_slip" is the total amount of slip in the constraint and "output_axial_plastic_slip" is the plastic component of the slip.

Example Input File Syntax

Listing 1: Example usage of ADRebarBondSlipConstraint. Note the AD terms are limited to the constraint and do not show up in other blocks.

[Constraints<<<{"href": "../../syntax/Constraints/index.html"}>>>]
  [rebar_x]
    type = ADRebarBondSlipConstraint<<<{"description": "Constraint using a physical model to enforce the bond-slip behavior between concrete and rebar.", "href": "RebarBondSlipConstraint.html"}>>>
    secondary<<<{"description": "secondary block id"}>>> = 2
    primary<<<{"description": "primary block id"}>>> = 1
    penalty<<<{"description": "Penalty parameter used in constraint enforcement for kinematic and penalty formulations."}>>> = 1e10
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = 'disp_x'
    primary_variable<<<{"description": "The variable on the primary side of the domain"}>>> = 'disp_x'
    max_bond_stress<<<{"description": "Maximum bond stress"}>>> = 1e6
    transitional_slip_value<<<{"description": "Transition between loading and frictional slip"}>>> = 5e-5
    rebar_radius<<<{"description": "Radius of the rebar"}>>> = 2.00e-4
    formulation<<<{"description": "Formulation used to enforce the constraint"}>>> = PENALTY
    bondslip_model<<<{"description": "Node-Element bond slip model."}>>> = concrete_rebar_model
    output_axial_slip<<<{"description": "Rebar axial slip output variable."}>>> = output_axial_slipx
    output_axial_force<<<{"description": "Rebar axial force output variable"}>>> = output_axial_forcex
    output_axial_plastic_slip<<<{"description": "Rebar axial plastic component of bond slip"}>>> = output_axial_plastic_slipx
  []
[]

Input Parameters

displacementsThe displacements appropriate for the simulation geometry and coordinate system
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements appropriate for the simulation geometry and coordinate system
max_bond_stressMaximum bond stress
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum bond stress
penaltyPenalty parameter used in constraint enforcement for kinematic and penalty formulations.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Penalty parameter used in constraint enforcement for kinematic and penalty formulations.
primaryprimary block id
C++ Type:SubdomainName
Controllable:No
Description:primary block id
primary_variableThe variable on the primary side of the domain
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The variable on the primary side of the domain
rebar_radiusRadius of the rebar
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Radius of the rebar
secondarysecondary block id
C++ Type:SubdomainName
Controllable:No
Description:secondary block id
transitional_slip_valueTransition between loading and frictional slip
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Transition between loading and frictional slip
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

bondslip_modelelastic_perfect_plastic_modelNode-Element bond slip model.
Default:elastic_perfect_plastic_model
C++ Type:MooseEnum
Options:concrete_rebar_model, elastic_perfect_plastic_model
Controllable:No
Description:Node-Element bond slip model.
formulationkinematicFormulation used to enforce the constraint
Default:kinematic
C++ Type:MooseEnum
Options:kinematic, penalty
Controllable:No
Description:Formulation used to enforce the constraint
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
output_axial_forceRebar axial force output variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Rebar axial force output variable
output_axial_plastic_slipRebar axial plastic component of bond slip
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Rebar axial plastic component of bond slip
output_axial_slipRebar axial slip output variable.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Rebar axial slip output variable.

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>
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>
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>
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
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
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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
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
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
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

References

G. Mehlhorn, J. Kollegger, M. Keuser, and W. Kolmar. Nonlinear contact problems - a finite element approach implemented in ADINA. Computers and Structures, 21():69–80, 1985.

@article{bondlsip_adina_1985,
    Author = "Mehlhorn, G. and Kollegger, J. and Keuser, M. and Kolmar, W.",
    Journal = "Computers and Structures",
    Number = "",
    Pages = "69--80",
    Title = "Nonlinear Contact Problems - A Finite Element Approach Implemented in {ADINA}",
    Volume = "21",
    Year = "1985"
}

(blackbear/test/tests/rebar_bondslip/RCBeam_elastic_constraint_45Deg.i)

[Mesh]
  [meshfile]
    type = FileMeshGenerator
    file = gold/RCBeam_test_mesh.e
  []
  [rotate]
    type = TransformGenerator
    input = meshfile
    transform = 'rotate'
    vector_value = '45 0 0'
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Modules]
  [TensorMechanics]
    [Master]
      [Concrete_block]
        block = 1
        strain = small
        incremental = true
        generate_output = 'stress_xx strain_xx'
      []
    []
  []
[]

[Physics]
  [SolidMechanics]
    [LineElement]
      [QuasiStatic]
        [Reinforcement_block]
          block = '2'
          truss = true
          area = area
          displacements = 'disp_x disp_y'
        []
      []
    []
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [area]
    order = CONSTANT
    family = MONOMIAL
  []
  [axial_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [axial_total_stretch]
    order = CONSTANT
    family = MONOMIAL
  []
  [axial_elastic_stretch]
    order = CONSTANT
    family = MONOMIAL
  []
  [output_axial_slipx]
  []
  [output_axial_forcex]
  []
  [output_axial_plastic_slipx]
  []
  [output_axial_slipy]
  []
  [output_axial_forcey]
  []
  [output_axial_plastic_slipy]
  []
[]

[AuxKernels]
  [area]
    type = ConstantAux
    block = '2'
    variable = area
    value = 2.00e-4
    execute_on = 'initial timestep_begin'
  []
  [axial_stress]
    type = MaterialRealAux
    block = '2'
    variable = axial_stress
    property = axial_stress
  []

  [axial_total_stretch]
    type = MaterialRealAux
    block = '2'
    property = total_stretch
    variable = axial_total_stretch
  []
  [axial_elastic_stretch]
    type = MaterialRealAux
    block = '2'
    property = elastic_stretch
    variable = axial_elastic_stretch
  []
[]

[Constraints]
  [rebar_x]
    type = ADRebarBondSlipConstraint
    secondary = 2
    primary = 1
    penalty = 1e10
    variable = 'disp_x'
    primary_variable = 'disp_x'
    max_bond_stress = 1e6
    transitional_slip_value = 5e-5
    rebar_radius = 2.00e-4
    formulation = PENALTY
    bondslip_model = concrete_rebar_model
    output_axial_slip = output_axial_slipx
    output_axial_force = output_axial_forcex
    output_axial_plastic_slip = output_axial_plastic_slipx
  []
  [rebar_y]
    type = ADRebarBondSlipConstraint
    secondary = 2
    primary = 1
    penalty = 1e10
    variable = 'disp_y'
    primary_variable = 'disp_y'
    max_bond_stress = 1e6
    transitional_slip_value = 5e-5
    rebar_radius = 2.00e-4
    formulation = PENALTY
    bondslip_model = concrete_rebar_model
    output_axial_slip = output_axial_slipy
    output_axial_force = output_axial_forcey
    output_axial_plastic_slip = output_axial_plastic_slipy
  []
[]

[Functions]
  [loading]
    type = PiecewiseLinear
    x = '0 10       20     30 '
    y = '0 ${fparse 0.00008/sqrt(2)} ${fparse -0.0001/sqrt(2)} 0.0'
  []
[]

[BCs]
  [loading_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = '102'
    function = loading
  []
  [loading_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = '102'
    function = loading
  []
  [left_support_x]
    type = DirichletBC
    variable = disp_x
    boundary = '100'
    value = 0
  []
  [left_support_y]
    type = DirichletBC
    variable = disp_y
    boundary = '100'
    value = 0
  []
[]

[Materials]
  [Cijkl_concrete]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 500e6
    poissons_ratio = 0.2
    block = '1'
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = '1'
  []
  [truss]
    type = LinearElasticTruss
    block = '2'
    youngs_modulus = 2e11
  []
[]

[Postprocessors]
  [stress_xx]
    type = ElementAverageValue
    variable = stress_xx
    block = '1'
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
    block = '1'
  []
  [axial_stress]
    type = ElementAverageValue
    variable = axial_stress
    block = '2'
  []
  [axial_elastic_stretch]
    type = ElementAverageValue
    variable = axial_elastic_stretch
    block = '2'
  []
  [axial_total_stretch]
    type = ElementAverageValue
    variable = axial_total_stretch
    block = '2'
  []
  [node_slipx]
    type = NodalVariableValue
    variable = output_axial_slipx
    nodeid = 152
  []
  [node_forcex]
    type = NodalVariableValue
    variable = output_axial_forcex
    nodeid = 152
  []
  [node_plastic_slipx]
    type = NodalVariableValue
    variable = output_axial_plastic_slipx
    nodeid = 152
  []
  [node_slipy]
    type = NodalVariableValue
    variable = output_axial_slipy
    nodeid = 152
    outputs = none
  []
  [node_forcey]
    type = NodalVariableValue
    variable = output_axial_forcey
    nodeid = 152
    outputs = none
  []
  [node_plastic_slipy]
    type = NodalVariableValue
    variable = output_axial_plastic_slipy
    nodeid = 152
    outputs = none
  []
  [compare]
    type = ParsedPostprocessor
    expression = 'abs(node_slipx-node_slipy)+abs(node_forcex-node_forcey)+abs(node_plastic_slipx-node_plastic_slipy)'
    pp_names = 'node_slipx node_forcex node_plastic_slipx node_slipy node_forcey node_plastic_slipy'
    outputs = none
  []
[]

[UserObjects]
  [terminate]
    type = Terminator
    expression = 'compare > 1e-10'
    error_level = ERROR
    message = 'x and y constraints are not producing equal values to requried tolerance.'
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  nl_max_its = 20
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-6
  line_search = none
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  petsc_options = '-snes_converged_reason'
  end_time = 30
  dt = 0.5
[]

[Outputs]
  csv = true
[]

Example Input File Syntax
Input Parameters
References

Usage

Development

Demonstration