Concrete Expansion Microcracking Damage

Scalar damage model based on extent of internal expansion

Description

The ConcreteExpansionMicrocrackingDamage model computes a scalar damage index $var element = document.getElementById("moose-equation-aa44dcd2-356a-4edc-b6d8-34ea470b9d58");katex.render("d", element, {displayMode:false,throwOnError:false});$ that increases with the progress of the eigenstrain defined by the eigenstrain_name input parameter (for example, the eigenstrain induced by alkali-silica reaction (ASR) using a ConcreteASREigenstrain model) and the current stress state of the material.

More specifically, this model is aimed at capturing anisotropic effects on ASR (and similar expansion mechanisms) without relying on an explicit redistribution of the eigenstrain itself. Instead, external stresses increase the damage so that the \emph{apparent} expansion is negated in the direction of the load. However, expansive eigenstrains are still applied in all directions. This model makes the following assumptions:

The eigenstrain is isotropic.
In an nconfined condition, the damage increases with the expansion.
When the compressive stress exceeds a predefined value $var element = document.getElementById("moose-equation-41311c7f-c157-4c74-a375-48faa98a5f69");katex.render("\\sigma_u", element, {displayMode:false,throwOnError:false});$ , the damage increases with the expansion so that the apaprent expansion is negated in the direction of the load.

In the following, $var element = document.getElementById("moose-equation-6001dd6c-d406-4fe9-8bd6-1c33f7f47b9a");katex.render("\\varepsilon_{lin}^{eig}", element, {displayMode:false,throwOnError:false});$ is the linear eigenstrain and $var element = document.getElementById("moose-equation-29681b02-87a5-45cc-a5ce-20deb7bf7cd8");katex.render("\\sigma_c", element, {displayMode:false,throwOnError:false});$ the compressive stress (measured as the sum of the negative components of the principal stress).

Unconfined Damage

In an unconfined condition $var element = document.getElementById("moose-equation-886412b1-eed8-4312-ba2e-24ccd3386fec");katex.render("(\\sigma_c = 0)", element, {displayMode:false,throwOnError:false});$ , the damage $var element = document.getElementById("moose-equation-bba6dc49-1edc-4f7e-ad21-63bd5e373115");katex.render("d_{unconfined}", element, {displayMode:false,throwOnError:false});$ depends only on the eigenstrain:

$(1)var element = document.getElementById("moose-equation-ae7a22d9-581e-48fd-82af-b1dd770548bf");katex.render(" d_{unconfined} = 1.0 - \\frac{\\varepsilon_{branch}}{\\varepsilon_{lin}^{eig} - (\\varepsilon_{branch} + \\varepsilon_{init})}", element, {displayMode:true,throwOnError:false});$

in which $var element = document.getElementById("moose-equation-816c6f8b-1882-4519-981f-7964c7c117a0");katex.render("\\varepsilon_{init}", element, {displayMode:false,throwOnError:false});$ is the linear expansion at which damage initiates and $var element = document.getElementById("moose-equation-e02f115e-5bc8-4368-a61c-9bf286dadaac");katex.render("\\varepsilon_{branch}", element, {displayMode:false,throwOnError:false});$ controls the rate at which damage increases with the eigenstrain.

Confined Damage

In a confined condition (when $var element = document.getElementById("moose-equation-04cb8815-3373-4823-9e4b-6f961452dfbb");katex.render("\\sigma_c > \\sigma_u", element, {displayMode:false,throwOnError:false});$ ), the damage is further increased so that the apparent expansion in the direction of the load The apparent expansion is defined by the difference between the current total strain (accounting for both the current damage and the eigenstrain itself), and the total strain that would be induced by the same stress on a pristine material (without expansion or damage). The damage $var element = document.getElementById("moose-equation-3cbf875a-4235-45c8-94db-d7c1084c44d3");katex.render("d_{confined}", element, {displayMode:false,throwOnError:false});$ is then obtained as:

$(2)var element = document.getElementById("moose-equation-9526d55c-a672-4462-8aaa-41c7188be6e5");katex.render(" d_{confined} = 1.0 - \\frac{1.0}{1.0 + \\frac{\\mathrm{E} \\varepsilon_{lin}^{eig}}{\\sigma_c}}", element, {displayMode:true,throwOnError:false});$

in which $var element = document.getElementById("moose-equation-d30f9747-dfa9-43bf-bffe-ec2288055306");katex.render("\\mathrm{E}", element, {displayMode:false,throwOnError:false});$ is the Young's modulus of the pristine concrete.

The effect of stress on the damage can be disabled by setting the use_stress_control input parameter to false.

Mixed Conditions

When $var element = document.getElementById("moose-equation-a79f2d91-5f02-4d7c-9576-774a05843f71");katex.render("\\sigma_c", element, {displayMode:false,throwOnError:false});$ is between $var element = document.getElementById("moose-equation-b1ce49a9-57bd-4768-bdfa-1055f343aefd");katex.render("0", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-a4e300bf-f3be-4bc1-85aa-b60889899453");katex.render("\\sigma_u", element, {displayMode:false,throwOnError:false});$ , the overall damage is taken as a linear combination of the increment of unconfined and confined damage:

$(3)var element = document.getElementById("moose-equation-ce3d74f7-b947-4edf-883b-575ce864e770");katex.render(" d = \\left( 1 - \\frac{\\sigma_c}{\\sigma_u} \\right) d_{unconfined} + \\frac{\\sigma_c}{\\sigma_u} d_{confined}", element, {displayMode:true,throwOnError:false});$

Anisotropic Eigenstrain

This model can accomodate for anisotropic eigenstrain by setting the use_isotropic_expansion input parameter to false, even though doing so is not recommended. In this condition, $var element = document.getElementById("moose-equation-76bf733e-d5cc-4b3e-865d-d78ce008f90a");katex.render("\\varepsilon_{lin}^{eig}", element, {displayMode:false,throwOnError:false});$ is defined as the maximum principal component of the eigenstrain.

Implementation and Usage

This model only computes a scalar damage index, and must rely on an external model to compute the expansion. If a ConcreteASREigenstrain model (or similar model) is used to simulate ASR, then the expansion_type for the ASR model should be set to Isotropic. In order for the damage to be accounted for in the stress calculation, the stress needs to be computed using a ComputeDamageStress stress calculator.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [microcracking]
    type = ConcreteExpansionMicrocrackingDamage<<<{"description": "Scalar damage model based on extent of internal expansion", "href": "ConcreteExpansionMicrocrackingDamage.html"}>>>
    microcracking_eigenstrain_name<<<{"description": "Name of the eigenstrain driving the microcracking damage process"}>>> = concrete_expansion
    microcracking_initiation_strain<<<{"description": "Linear strain at which the microcracking initiates (in [m/m])"}>>> = 0.0001
    microcracking_strain_branch<<<{"description": "Parameter controlling the rate at which the microcracking increases (in [m/m])"}>>> = 0.0002
  []
[]

Input Parameters

microcracking_eigenstrain_nameName of the eigenstrain driving the microcracking damage process
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Name of the eigenstrain driving the microcracking damage process
microcracking_initiation_strainLinear strain at which the microcracking initiates (in [m/m])
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Linear strain at which the microcracking initiates (in [m/m])
microcracking_strain_branchParameter controlling the rate at which the microcracking increases (in [m/m])
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Parameter controlling the rate at which the microcracking increases (in [m/m])

Required Parameters

assume_isotropic_expansionTrueIndicates whether the model assumes an isotropic expansion (true) or computes the linear expansion based on the first principal eigenstrain (false)
Default:True
C++ Type:bool
Controllable:No
Description:Indicates whether the model assumes an isotropic expansion (true) or computes the linear expansion based on the first principal eigenstrain (false)
base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
damage_index_namedamage_indexname of the material property where the damage index is stored
Default:damage_index
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:name of the material property where the damage index is stored
declare_suffixAn optional suffix parameter that can be appended to any declared 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 declared properties. The suffix will be prepended with a '_' character.
eigenstrain_factor1Correction factor by which the eigenstrain is multiplied before evaluating the damage
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Correction factor by which the eigenstrain is multiplied before evaluating the damage
expansion_stress_limitUpper bound compressive stress beyond which damage is controlled by the external stress
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Upper bound compressive stress beyond which damage is controlled by the external stress
include_confinement_effectsTrueIndicates whether the damage is affected by the current stress state
Default:True
C++ Type:bool
Controllable:No
Description:Indicates whether the damage is affected by the current stress state
maximum_damage1Maximum value allowed for damage index
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum value allowed for damage index
maximum_damage_increment0.1maximum damage increment allowed for simulations with adaptive time step
Default:0.1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:maximum damage increment allowed for simulations with adaptive time step
residual_stiffness_fraction1e-08Minimum fraction of original material stiffness retained for fully damaged material (when damage_index=1)
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Minimum fraction of original material stiffness retained for fully damaged material (when damage_index=1)
use_old_damageFalseWhether to use the damage index from the previous step in the stress computation
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use the damage index from the previous step in the stress computation

Optional 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
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

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

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.
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
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.

Material Property Retrieval Parameters

References

No citations exist within this document.

(blackbear/test/tests/concrete_expansion_microcracking/concrete_expansion_microcracking.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  elem_type = HEX8
[]


[AuxVariables]
  [./expansion_vstrain]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./expansion_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./expansion_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./expansion_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./microcracking]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./damage_index]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Functions]
  [./expansion_vs_time]
    type = ParsedFunction
    expression = 'max(0, t - 0.0001)'
  [../]
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = SMALL
        incremental = true
        add_variables = true
        generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
        eigenstrain_names = 'concrete_expansion'
      []
    []
  []
[]


[AuxKernels]
  [./expansion_vstrain]
    type = MaterialRealAux
    variable = expansion_vstrain
    property = test_volumetric_strain
    execute_on = 'timestep_end'
  [../]
  [./expansion_strain_xx]
    type = RankTwoAux
    rank_two_tensor = concrete_expansion
    variable = expansion_strain_xx
    index_i = 0
    index_j = 0
    execute_on = 'timestep_end'
  [../]
  [./expansion_strain_yy]
    type = RankTwoAux
    rank_two_tensor = concrete_expansion
    variable = expansion_strain_yy
    index_i = 1
    index_j = 1
    execute_on = 'timestep_end'
  [../]
  [./expansion_strain_zz]
    type = RankTwoAux
    rank_two_tensor = concrete_expansion
    variable = expansion_strain_zz
    index_i = 2
    index_j = 2
    execute_on = 'timestep_end'
  [../]
  [./damage_index]
    type = MaterialRealAux
    variable = damage_index
    property = damage_index
    execute_on = 'timestep_end'
  [../]
[]

[BCs]
  [./symmx]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./symmy]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
  [./symmz]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0
  [../]

  [./load_x]
    type = NeumannBC
    variable = disp_x
    boundary = right
    value    = 0
  [../]
  [./load_y]
    type = NeumannBC
    variable = disp_y
    boundary = top
    value    = 0
  [../]
  [./load_z]
    type = NeumannBC
    variable = disp_z
    boundary = front
    value    = 0
  [../]
[]

[Materials]
  [microcracking]
    type = ConcreteExpansionMicrocrackingDamage
    microcracking_eigenstrain_name = concrete_expansion
    microcracking_initiation_strain = 0.0001
    microcracking_strain_branch = 0.0002
  []

  [stress]
    type = ComputeDamageStress
    damage_model = microcracking
  []

  [./concrete]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 30e9
    poissons_ratio = 0.2
  [../]

  [concrete_expansion]
    type = TestConcreteExpansionEigenstrain
    expansion_type = Isotropic
    function = expansion_vs_time
    eigenstrain_name = concrete_expansion
  []
[]

[Postprocessors]
  [./expansion_vol_strain]
    type = ElementAverageValue
    variable = expansion_vstrain
  [../]
  [./expansion_strain_xx]
    type = ElementAverageValue
    variable = expansion_strain_xx
  [../]
  [./stress_xx]
    type = ElementAverageValue
    variable = stress_xx
  [../]
  [./strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  [../]
  [./expansion_strain_yy]
    type = ElementAverageValue
    variable = expansion_strain_yy
  [../]
  [./stress_yy]
    type = ElementAverageValue
    variable = stress_yy
  [../]
  [./strain_yy]
    type = ElementAverageValue
    variable = strain_yy
  [../]
  [./expansion_strain_zz]
    type = ElementAverageValue
    variable = expansion_strain_zz
  [../]
  [./stress_zz]
    type = ElementAverageValue
    variable = stress_zz
  [../]
  [./strain_zz]
    type = ElementAverageValue
    variable = strain_zz
  [../]
  [./damage_index]
    type = ElementAverageValue
    variable = damage_index
  [../]
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_max_its  = 50
  l_tol      = 1e-6
  nl_max_its = 20
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10

  start_time = 0
  dt = 0.0001
  dtmin = 0.0001
  end_time = 0.0011
[]

[Outputs]
  file_base = concrete_expansion_microcracking_out
  csv = true
[]

Description
Implementation and Usage
Example Input Syntax
Input Parameters
References

Usage

Development

Demonstration