TensorMechanics coupling

[walkand...@gmail.com]

Dear all,

    I'm trying to use Moose's TensorMechanics module, it is really powerful.

    In my model, I have a stress field and concentration field.

    

    For the small strain elastic problem, the governing equation looks like:

where the epsilon is the small elastic strain defined as epsilon=(\nabla u+u\nabla^T)/2, c is the concentration.

For the diffusion problem, its governing equation looks like:

Now, I can use the TensorMechanics module for the first equation, and then define the strain depend on C. For the diffusion problem, I used a AuxKernel to compute the hydrostatic stress and use it as a coupled variable for the diffusion equaiton. Here is my input file:

******************************************

[Kernels]

  [./TensorMechanics]

    displacements = 'disp_x disp_y'

    use_displaced_mesh = false

  [../]

  [./ctime]

    type = TimeDerivative

    variable = c

  [../]

  [./diff]

    type = ExampleC

    variable =c

    D = 0.1

    couple_stress = hystress

  [../]

[]

[Materials]

  [./elasticity_tensor]

    type = ComputeIsotropicElasticityTensor

    youngs_modulus = 2.1e0

    poissons_ratio = 0.3

    use_displaced_mesh = false

  [../]

  [./strain]

    type = ComputeSmallStrain

    displacements = 'disp_x disp_y'

    eigenstrain_names = eigen_c

  [../]

  [./eigen_strain]

    type = ComputeVariableEigenstrain

    args = c

    eigen_base = '1 1 1 0 0 0'

    eigenstrain_name = eigen_c

    outputs = exodus

  [../]

  [./stress]

    type = ComputeLinearElasticStress

  [../]

[]

[AuxVariables]

  [./hystress]

    family = MONOMIAL

    order = FIRST

  [../]

[]

[AuxKernels]

  [./gethystress]

    type = RankTwoScalarAux

    rank_two_tensor = stress

    variable = hystress

    scalar_type = Hydrostatic

  [../]

[]

***************************************

In the [Materials] block, I tried to calculate the strain based on c(use the ComputeVariableEigenstrain), but this is just like one way coupling right? No contribution for K_{uc} ?

I think the final system matrix should be like the following right?

So I'm wondering:

1. TensorMechanic module is really powerful, so I want to use it for the elastic part, let's say the K_{uu} , then for the coupling part, is it possible that

I create a C++ class and inherit from TensorMechanics, and override the computeQpOffDiagnoalJacobian() function, then I can do the computation for K{uc}?

    

    I tried to #include "TensorMechaincs.h", but it seems I go to the wrong direction.

maybe there should have another better solutions for such kind problems.

2. For the diffusion part, K_{cc} is ok, very easy to implemenet. But for the K_{cu} part, since there the u is a vector, so inside the computeQpOffDiagnalJacobian function

we should give 

  if (jvar==_couple_sigma_var)

 {

     K_{cu}=(dR_{c}/dSigma)*(dSigma/du)

 }

this makes me confused, if we do the assemble things one by one, the K_{cu} term should take two positions right?

3. Is there any other examples or solutions for such TensorMechanics based coupling problem?  Any helpful suggestion is welcome!

Thank you all.

Best regards

[Daniel Schwen]

c_ref does not seem to appear in your moose model. ComputeVariableEigenstrain requires a DerivativeParsedMaterial 'prefactor' argument! (that material would implement the c- c_ref term).

--
You received this message because you are subscribed to the Google Groups "moose-users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to moose-users...@googlegroups.com.
Visit this group at https://groups.google.com/group/moose-users.
To view this discussion on the web visit https://groups.google.com/d/msgid/moose-users/6ee62f68-f840-479c-8c19-8deb045c06fc%40googlegroups.com.
For more options, visit https://groups.google.com/d/optout.

[nicolog...@gmail.com]

You should look at the phase field fracture example. It is similar to what you are doing. c in that case is a damage phase field. It is in the tests of the tensor mechanics module and you can see how to add a piece of the Jacobian to the tensor mechanics part

[walkand...@gmail.com]

在 2017年9月22日星期五 UTC+2下午5:22:16，Daniel Schwen写道：

c_ref does not seem to appear in your moose model. ComputeVariableEigenstrain requires a DerivativeParsedMaterial 'prefactor' argument! (that material would implement the c- c_ref term).

Hi Daniel, 

  Thank you sincerely for the reply. Follow your suggestion, now I can apply the eigen strain to the mechanical part. 

  I modified my input file as follow:

****************************************

[Materials]

  [./elasticity_tensor]

    type = ComputeIsotropicElasticityTensor

    youngs_modulus = 14.8619240917

    poissons_ratio = 0.3

    use_displaced_mesh = false

  [../]

  [./strain]

    type = ComputeSmallStrain

    displacements = 'disp_x disp_y'

    eigenstrain_names = eigen_c

  [../]

  [./eigen_f]

    type = DerivativeParsedMaterial

    function = (c-0.5)/3.0

    f_name = f

    args = c

  [../]

  [./eigen_strain]

    type = ComputeVariableEigenstrain

    args = c

    eigen_base = '1 1 1 0 0 0'

    prefactor = f

    eigenstrain_name = eigen_c

    outputs = exodus

  [../]

  [./stress]

    type = ComputeLinearElasticStress

  [../]

[]

****************************************

I think it is correct, right? Where I take C_ref=0.5,Omega=1, the final strain is epsilon-(c-c_ref)/3*I ,I treat the (c-c_ref) as the pfactor, since I see in the code,

// Remove the Eigen strain

57  for (auto es : _eigenstrains)

58  _mechanical_strain[_qp] -= (*es)[_qp];

where I guess the es represent the eigen strain, it is computed via:

_eigenstrain[_qp] = _eigen_base_tensor * _prefactor[_qp]

If I'm right, the TensorMechanics kernel used the small strain and C defined eigen strain to calculate the stress and do the simulation, has it also some contributions to the K_{uc} part? It looks like the one way coupling?

I checked several input files in modules/tensor_mechanics/test/tests/, there are many examples, that's really perfect. But I don't find these "OffDiagnal" things.

I followed nicolog's suggestion, and find that in  modules/combined/test/tests/phase_field_fracture/, the phase field method based fracture model's input file has such things, where it looks like:

**************************************

[./solid_x]

    type = PhaseFieldFractureMechanicsOffDiag

    variable = disp_x

    component = 0

    c = c

  [../]

  [./solid_y]

    type = PhaseFieldFractureMechanicsOffDiag

    variable = disp_y

    component = 1

    c = c

  [../]

**************************************

I think this is the coupling term: 

K_{Ux C}=(dR_ux/dc)

K_{Uy C}=(dR_uy/dc)

right?

Is it possible that I don't use the PhaseFieldFractureMechanicsOffDiag kernel(or module), but still can compute these OffDiag term, such as K_{uc}?

And how about these K{CU} term? the K_{cUx},K_{cUy}?

Thank you so much!

Best regards

[walkand...@gmail.com]

Hi nicolog,

Thank you so much for the reply.

Your suggestion is really helpful.

I find the fracture model's test input file in  modules/combined/test/tests/phase_field_fracture/, the phase field method based fracture model's input file has such things, where it looks like:

**************************************

[./solid_x]

    type = PhaseFieldFractureMechanicsOffDiag

    variable = disp_x

    component = 0

    c = c

  [../]

  [./solid_y]

    type = PhaseFieldFractureMechanicsOffDiag

    variable = disp_y

    component = 1

    c = c

  [../]

**************************************

I think this is the coupling term: 

K_{Ux C}=(dR_ux/dc)

K_{Uy C}=(dR_uy/dc)

right?

It seems this is only for the PhaseFieldFracture kernel, is it possible that I don't use the PhaseFieldFractureMechanicsOffDiag kernel(or module), but still can compute these OffDiag term, such as K_{uc}? 

And how about these K{cU} term, the K_{cUx},K_{cUy}?

Best regards

在 2017年9月23日星期六 UTC+2下午1:33:22，nicolog...@gmail.com写道：

[nicolog...@gmail.com]

Yes, PhaseFieldFractureMechanicsOffDiag computes the derivative of the displacement residual with respect to the phase field c (dR_ux/dc and dR_uy/dc)
You will have to write a new similar kernel that does that for your particular model.
The FDP preconditioner can calculate the Jacobian without you implementing an analytical expression, but this is slow.
I strongly suggest you to implement the kernel to calculate your off-diagonal terms, follow the instructions:
http://mooseframework.org/static/media/uploads/files/MOOSEPF_MARMOT_training_1_recap.pdf
http://mooseframework.org/wiki/MooseTraining/MultiphysicsCoupling/

[walkand...@gmail.com]

Thank you Nicolog, this is really helpful for me!

Best regard

在 2017年9月25日星期一 UTC+2下午1:21:38，nicolog...@gmail.com写道：