Compute Interface Stress

Stress in the plane of an interface defined by the gradient of an order parameter

Description

The resulting stress tensor has the property of having one Eigenvector in the direction of the order parameter gradient, with an Eigenvalue of zero, and two Eigenvectors perpendicular to that direction, with an Eigenvalue $var element = document.getElementById("moose-equation-29f14827-f18e-4713-b683-01f11a3a7d40");katex.render("\\sigma_i\\cdot|\\nabla\\eta|", element, {displayMode:false,throwOnError:false});$ , where the scalar $var element = document.getElementById("moose-equation-73910aaf-a78e-4f0c-bea3-b037789d1a31");katex.render("\\sigma_i", element, {displayMode:false,throwOnError:false});$ (stress) is a supplied parameter and $var element = document.getElementById("moose-equation-b2959da8-009f-4df2-b5c8-b70939c760c5");katex.render("\\eta", element, {displayMode:false,throwOnError:false});$ (v) is a given order parameter. $var element = document.getElementById("moose-equation-d0e3d7a6-1be2-4490-a0a2-6d9108f66d4c");katex.render("\\vec e_1 = \\frac{\\nabla\\eta}{|\\nabla\\eta|}", element, {displayMode:true,throwOnError:false});$

Then two more linearly independent vectors $var element = document.getElementById("moose-equation-e00feabb-56c7-45e7-ba73-dc763257a04e");katex.render("\\vec e_2", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-c8e2df99-1989-4594-a8fa-2049dcd44104");katex.render("\\vec e_3", element, {displayMode:false,throwOnError:false});$ are generated by determining the component $var element = document.getElementById("moose-equation-d200c2df-7125-497a-80e5-ddb0a56f5cb0");katex.render("m", element, {displayMode:false,throwOnError:false});$ of $var element = document.getElementById("moose-equation-08258d79-fff2-4f18-8160-9dc9af3714ee");katex.render("\\vec e_1", element, {displayMode:false,throwOnError:false});$ with the largest magnitude. $var element = document.getElementById("moose-equation-30f92840-556b-467c-8bc1-1ded8e0702f8");katex.render("\\vec e_2", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-10a6dab2-a0b4-4875-9a27-1d73010d58dd");katex.render("\\vec e_3", element, {displayMode:false,throwOnError:false});$ are then set to unit vectors from the set $var element = document.getElementById("moose-equation-ff98b848-85f3-4e00-8286-abf8f4fa09f6");katex.render("\\vec u_1 = (1,0,0), \\vec u_2 = (0,1,0), \\vec u_3 = (0,0,1)", element, {displayMode:true,throwOnError:false});$ such that $var element = document.getElementById("moose-equation-23dd62db-ec42-4a67-ad7a-2068230ba067");katex.render("\\vec e_2 = \\vec u_{(m+1) \\backslash{3}}, \\vec e_3 = \\vec u_{(m+2)\\backslash{3}},", element, {displayMode:true,throwOnError:false});$ where the $var element = document.getElementById("moose-equation-86ca09b5-36dc-4820-81a8-1d7e27eed05f");katex.render("\\backslash", element, {displayMode:false,throwOnError:false});$ operator represents integer modulo. The basis $var element = document.getElementById("moose-equation-d812ba5e-f8e2-4ab8-b59a-0de0a8e7dae7");katex.render("\\vec e_i", element, {displayMode:false,throwOnError:false});$ is then orthonormalized using the modified Gram-Schmidt procedure, holding $var element = document.getElementById("moose-equation-c6c436ca-448d-4b60-bc1a-9c86476e4877");katex.render("\\vec e_1", element, {displayMode:false,throwOnError:false});$ constant. We construct two matrices $var element = document.getElementById("moose-equation-c279465f-ee4d-4b2d-836a-d067dce8272b");katex.render("\\boldsymbol{M} = \\left( \\begin{matrix} 0 & 0 & 0 \\\\ 0 & \\sigma_i & 0 \\\\ 0 & 0 & \\sigma_i \\end{matrix} \\right), \\boldsymbol{S}= \\left( \\begin{matrix} \\vec e_1 & \\vec e_2 & \\vec e_3 \\end{matrix} \\right),", element, {displayMode:true,throwOnError:false});$ and set the stress tensor $var element = document.getElementById("moose-equation-d9278ea7-d503-4710-9fe4-be238746f76f");katex.render("\\boldsymbol{\\sigma}", element, {displayMode:false,throwOnError:false});$ to $var element = document.getElementById("moose-equation-db74bdd8-2e9d-4952-813d-ad25954fcf80");katex.render("\\boldsymbol{\\sigma} = \\left(S\\cdot M\\cdot S^{-1}\\right)\\cdot|\\nabla\\eta|,", element, {displayMode:true,throwOnError:false});$ which is a basis transformation from the Eigenvector basis into the cartesian basis. The $var element = document.getElementById("moose-equation-df5bc4f4-a4b2-4e91-9c48-208bcec664f7");katex.render("|\\nabla\\eta|", element, {displayMode:false,throwOnError:false});$ factor causes the integral over the stress tensor across the interface to evaluate the same value, regardless of interfacial width (provided the order parameter range is well defined - commonly 0 and 1 on the two sides of the interface).

Example Input File Syntax

[./interface]
  type = ComputeInterfaceStress
  v = eta
  stress = 3.0
[../]

Input Parameters

stressInterfacial planar stress magnitude (one value to apply to all order parameters or one value per order parameter listed in 'v')
C++ Type:std::vector<double>
Controllable:No
Description:Interfacial planar stress magnitude (one value to apply to all order parameters or one value per order parameter listed in 'v')

Required Parameters

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
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
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
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
op_range1 Range over which order parameters change across an interface. By default order parameters are assumed to vary from 0 to 1
Default:1
C++ Type:std::vector<double>
Controllable:No
Description:Range over which order parameters change across an interface. By default order parameters are assumed to vary from 0 to 1
planar_stress_nameextra_stressMaterial property name for the interfacial planar stress
Default:extra_stress
C++ Type:MaterialPropertyName
Controllable:No
Description:Material property name for the interfacial planar stress
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
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.
vOrder parameters that define the interface. The interface is the region where the gradient of this order parameter is non-zero.
C++ Type:std::vector<VariableName>
Controllable:No
Description:Order parameters that define the interface. The interface is the region where the gradient of this order parameter is non-zero.

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

(moose/modules/tensor_mechanics/test/tests/interface_stress/test.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  ny = 10
  nz = 10
  xmax = 1
  ymax = 1
  zmax = 1
  xmin = -1
  ymin = -1
  zmin = -1
[]

[GlobalParams]
  order = CONSTANT
  family = MONOMIAL
  rank_two_tensor = extra_stress
[]

[Functions]
  [./sphere]
    type = ParsedFunction
    expression = 'r:=sqrt(x^2+y^2+z^2); if(r>1,0,1-3*r^2+2*r^3)'
  [../]
[]

[Variables]
  [./dummy]
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = dummy
  [../]
[]

[AuxVariables]
  [./eta]
    [./InitialCondition]
      type = FunctionIC
      function = sphere
    [../]
    order = FIRST
    family = LAGRANGE
  [../]
  [./s00]
  [../]
  [./s01]
  [../]
  [./s02]
  [../]
  [./s10]
  [../]
  [./s11]
  [../]
  [./s12]
  [../]
  [./s20]
  [../]
  [./s21]
  [../]
  [./s22]
  [../]
[]

[AuxKernels]
  [./s00]
    type = RankTwoAux
    variable = s00
    index_i = 0
    index_j = 0
  [../]
  [./s01]
    type = RankTwoAux
    variable = s01
    index_i = 0
    index_j = 1
  [../]
  [./s02]
    type = RankTwoAux
    variable = s02
    index_i = 0
    index_j = 2
  [../]
  [./s10]
    type = RankTwoAux
    variable = s10
    index_i = 1
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    index_i = 1
    index_j = 1
  [../]
  [./s12]
    type = RankTwoAux
    variable = s12
    index_i = 1
    index_j = 2
  [../]
  [./s20]
    type = RankTwoAux
    variable = s20
    index_i = 2
    index_j = 0
  [../]
  [./s21]
    type = RankTwoAux
    variable = s21
    index_i = 2
    index_j = 1
  [../]
  [./s22]
    type = RankTwoAux
    variable = s22
    index_i = 2
    index_j = 2
  [../]
[]

[Materials]
  [./interface]
    type = ComputeInterfaceStress
    v = eta
    stress = 3.0
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  hide = 'dummy eta'
[]