Explicit Time Integration in MASTODON

[Mriganabh]

Hi all,

I changed the beta values from 0.25 to 0 in example 1 for explicit time integration. Since I have specified any dtmin, I assumed the dt will be halved till convergence. But convergence is not achieved even when dt = 1e-14.

Do I need to make any other changes apart from beta (0.25 to 0)?

I have attached the input file for reference.

Thanks,

Mriganabh

[Chandrakanth Bolisetti]

Hi Mriganabh,

 

You cannot change beta and gamma to achieve explicit time integration in MASTODON, although that makes sense on paper. Explicit requires a lot more changes in the framework and we recently developed a Central Difference explicit integrator for that purpose. It will be available for everyone in a week or so.

 

Chandu

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[Mriganabh]

Thanks for the clarification, Chandu.

Best,

Mriganabh

On Monday, February 17, 2020 at 6:22:49 PM UTC-5, Chandrakanth Bolisetti wrote:

Hi Mriganabh,

 

You cannot change beta and gamma to achieve explicit time integration in MASTODON, although that makes sense on paper. Explicit requires a lot more changes in the framework and we recently developed a Central Difference explicit integrator for that purpose. It will be available for everyone in a week or so.

 

Chandu

 

 

From: mastodon-users <mastodo...@googlegroups.com> on behalf of Mriganabh <mrigan...@gmail.com>
Date: Monday, February 17, 2020 at 3:52 PM
To: mastodon-users <mastodo...@googlegroups.com>
Subject: [EXTERNAL] [mastodon-users] Explicit Time Integration in MASTODON

 

Hi all,

 

I changed the beta values from 0.25 to 0 in example 1 for explicit time integration. Since I have specified any dtmin, I assumed the dt will be halved till convergence. But convergence is not achieved even when dt = 1e-14.

 

Do I need to make any other changes apart from beta (0.25 to 0)?

 

I have attached the input file for reference.

 

Thanks,

Mriganabh

 

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[Mriganabh]

Hi Chandu,

I was wondering if the Central Difference explicit integrator is available. If yes, where can I find some documentation or examples?

Thanks,

Mriganabh

[Chandrakanth Bolisetti]

Hi Mriganabh,

 

It is not available yet. The MOOSE team has some final touches to do before it gets merged.

 

What do you plan to use it for?

 

Chandu

 

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From: mastodon-users <mastodo...@googlegroups.com> on behalf of Mriganabh <mrigan...@gmail.com>

Date: Monday, March 23, 2020 at 4:23 PM
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[Mriganabh]

Hi Chandu,

I apologize for the late reply. 

I figured out how to use run simulations using explicit time integration. I have attached the input file and mesh file as a reference for future users. The model descriptions are available in the attached PDF. 

I was able to achieve identical results when using implicit time integration. I also compared the results with ABAQUS/Standard & ABAQUS/Explicit and there were minor discrepancies.

Let me know if you have any questions.

Thanks,

Mriganabh

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[Chandrakanth Bolisetti]

Mriganabh,

 

Glad you figured it out. Thank you for sharing the input files with the group. If you are interested in creating a MASTODON example that goes on to the website, please let us know and we can help you do that. Since the central difference integrator is now merged into MOOSE, Som is about to publish some examples as well. You can also use the criticaltimestepcalculator object to automatically enforce the critical time step when using explicit.

 

Also, I noticed that you used the lumped mass option. Do the lumped mass results match well with Abaqus? Note that you cannot use the lumped mass option if you are using the NewmarkBeta time integrator. So if you are comparing implicit and explicit results, you can only do that using consistent mass.

 

Best regards,

Chandu

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[Mriganabh]

Hi Chandu,

Thank you for the suggestions and I would love to create a Mastodon example. Let me know about the procedure. You can contact me on mbo...@purdue.edu or (765)-413-6785.

Yes. There were discrepancies between lumped Central Difference and ABAQUS/Explicit (with Full Integration & Linear & Quadratic Bulk Viscosity Parameters set to zero). In Mastodon, I am requesting the stress time-history at a particular point (say 0, 0, 20) whereas, in ABAQUS, the stress-history from one of the integration points closest to (0, 0, 20), since all of them identical stress-history.

I have shared the ABAQUS input file and the results from MASTODON & ABAQUS/Explicit.

Let me know if you have any other questions.

Thanks,

Mriganabh

On Monday, February 17, 2020 at 5:50:35 PM UTC-5, Mriganabh wrote:

[Chandu Bolisetti]

Hi Mriganabh, 

I went through the results and it looks like ABAQUS and MASTODON results are quite different. Do you know if ABAQUS is using lumped or consistent mass? Also did you compare the results with a consistent mass matrix? Those should match much better.

You might know this at this point, but lumped and consistent formulations will provide consideraby different results unless the mesh is very fine. 

Best regards,

Chandu

[Mriganabh]

Hi Chandu,

ABAQUS uses lumped mass matrix for first-order elements (HEX8). Using a consistent mass matrix in MASTODON (Explicit) results in an even worse match when compared to ABAQUS/Explicit. 

I also looked at HEX20 in both MASTODON & ABAQUS. ABAQUS/Standard uses a consistent mass matrix for second-order elements (HEX20). ABAQUS/Explicit does not support HEX20 elements. Hence, I have compared the results of ABAQUS/Standard with both implicit & explicit time integration (with Consistent mass matrix) in MASTODON. These seem to match much better than HEX8 elements.

Let me know if you have any questions.

Thanks,

Mriganabh

[Chandrakanth Bolisetti]

Hi Mriganabh,

 

Yes, you should only compare lumped with lumped or consistent with consistent. If the lumped results are not matching well, there might be a difference in how the matrices are lumped in ABAQUS and MASTODON. MOOSE/MASTODON perform direct mass lumping, which results in a diagonal mass matrix. This is the simplest approach to mass lumping and I wouldn’t be surprised if ABAQUS does something more complex. Is there any information on how ABAQUS performs mass lumping? Also, I think this comparison should be made for a much smaller problem (may be even 1 element).

 

--

Best regards,

Chandu

 

From: mastodon-users <mastodo...@googlegroups.com> on behalf of Mriganabh <mrigan...@gmail.com>
Date: Monday, July 6, 2020 at 1:15 PM
To: mastodon-users <mastodo...@googlegroups.com>
Subject: [EXTERNAL] [mastodon-users] Re: Explicit Time Integration in MASTODON

 

Hi Chandu,

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[Mriganabh]

Hi Chandu,

The following is from the ABAQUS theory manual from section 2.4.1-3 -
------
The first-order elements in Abaqus all use “lumped” mass, where the mass
matrix is a diagonal matrix. The lumped matrix is obtained by adding each row of the consistent matrix onto
the diagonal. For these first-order elements the lumped mass matrix gives more accurate results in numerical experiments that calculate the natural frequencies of simple models.
-------
According to this, even abaqus uses direct mass lumping. I can run the same tests on a single element and see if I get identical results with ABAQUS & MASTODON.

Thanks,
Mriganabh

[Chandrakanth Bolisetti]

Mriganabh,

That is interesting. Thank you for checking. Yes, it would be better to perform this comparison for a very small model for which you can print out the mass matrix and compare element by element. If the mass matrices are the same, then the differences must be from something else.

--
Best regards,
Chandu

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[Mriganabh]

Hi Chandu,

Can you tell me how to print out the mass matrix in MASTODON?

Thanks,

Mriganabh

On Monday, July 6, 2020 at 4:08:14 PM UTC-4, Chandrakanth Bolisetti wrote:

Mriganabh,

That is interesting. Thank you for checking. Yes, it would be better to perform this comparison for a very small model for which you can print out the mass matrix and compare element by element. If the mass matrices are the same, then the differences must be from something else.

--
Best regards,
Chandu

On 7/6/20, 2:06 PM, "mastodo...@googlegroups.com on behalf of Mriganabh" <mastodo...@googlegroups.com on behalf of mrigan...@gmail.com> wrote:

    Hi Chandu,

    The following is from the ABAQUS theory manual from section 2.4.1-3  -
    ------
    The first-order elements in Abaqus all use “lumped” mass, where the mass
    matrix is a diagonal matrix. The lumped matrix is obtained by adding each row of the consistent matrix onto
    the diagonal. For these first-order elements the lumped mass matrix gives more accurate results in numerical experiments that calculate the natural frequencies of simple models.
    -------
    According to this, even abaqus uses direct mass lumping. I can run the same tests on a single element and see if I get identical results with ABAQUS & MASTODON.

    Thanks,
    Mriganabh

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[Chandrakanth Bolisetti]

Hi Mriganabh,

 

You can go to ExplicitTimeIntegrator.C in moose and add print out the _mass_matrix_diag variable after line 112. Simply add the line below, and compile mastodon.

 

      std::cout << _mass_matrix_diag;

 

When you run any problem with central difference timeintegrator, the mass matrix will be printed out at every time step. Note that since it is a diagonal matrix, it is stored as a vector with the diagonal values and therefore, you’ll see a vector output.   

--

Best regards,

Chandu

 

From: mastodon-users <mastodo...@googlegroups.com> on behalf of Mriganabh <mrigan...@gmail.com>

Date: Monday, July 6, 2020 at 4:13 PM
To: mastodon-users <mastodo...@googlegroups.com>

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[Mriganabh]

Hi Chandu,

Upon printing out the mass vector in MASTODON & the mass matrix in ABAQUS, I found that the mass vector in MASTODON has only 8 occupied entries of the 24 (DOFs) whereas in ABAQUS all the 24 DOFs are identical.

The difference in the order of magnitude is due to MASTODON & ABAQUS using different sets of units.

Let me know if you have any questions.

Thanks,

Mriganabh

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[Chandrakanth Bolisetti]

Mriganabh,

 

The difference is because of how MOOSE handles boundary conditions. The 1 in the matrix is because there is probably because there’s a Dirichlet BC in that dof. It looks like MASTODON and ABAQUS actually have the correct mass matrix here.

 

--

Best regards,

Chandu

 

From: mastodon-users <mastodo...@googlegroups.com> on behalf of Mriganabh <mrigan...@gmail.com>
Date: Tuesday, July 7, 2020 at 10:44 AM
To: mastodon-users <mastodo...@googlegroups.com>
Subject: Re: [EXTERNAL] [mastodon-users] Re: Explicit Time Integration in MASTODON

 

Hi Chandu,

 

Upon printing out the mass vector in MASTODON & the mass matrix in ABAQUS, I found that the mass vector in MASTODON has only 8 occupied entries of the 24 (DOFs) whereas in ABAQUS all the 24 DOFs are identical.

 

The difference in the order of magnitude is due to MASTODON & ABAQUS using different sets of units.

 

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[Mriganabh]

Hi Chandu,

Sounds good. I am not sure if I could find the reason behind discrepancies between ABAQUS/Explicit & Central Difference in Mastodon. However, as I had stated earlier, the results with HEX20 elements where all -  ABAQUS/Standard, Mastodon/Implicit & Mastodon/Explicit use consistent mass matrix produce much better matching.

Also, I would like to create a Mastodon example (related to Central Difference Time integration & using HEX20 elements) if it is fine by the developers at this point in time. 

Let me know if you have any questions.

Thanks,

Mriganabh

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[Christopher Wong]

Mriganabh,

I think you should just use HEX8 elements in your example for the CDM. There’s no need to introduce that extra layer of complexity brought out by higher order elements. The example should be about demonstrating the use of explicit integration for a simple and generic model, even just one HEX8 element, as Chandu suggested.

I’m trying to understand this evaluation you’re conducting. In my personal opinion, the percent difference between MASTODON and Abaqus should be roughly zero. Someone is making a mistake here, and I’m going to guess that it’s the user (us) and not the developers.

First of all, if you’re using HEX20 elements, you need to use quadratic polynomials to interpolate the displacements, that is, you should set `order = second` in the displacement blocks. If you use HEX8, you need to use linear, which is the default. You might do the same for your auxiliary variables, although it won’t affect the primary solution.

Second, how exactly did you produce those plots shown in your PDFs? Where is this transient vibration response coming from? All I see is a quastistatic pressure load in your input. Could you please provide all the relevant input files and identify what you’re modeling with them?

Third, what comparisons are you trying to make here, I’m seeing terms like: Abaqus standard, Abaqus explicit, central difference method, implicit, lumped mass, consistent mass, HEX8, HEX20, etc., but I have no idea what combination of these things your verifications are using. Could you please disambiguate the difference between your models please?

Fourth, let’s take this one test at a time. It seems like you should be using hex8 elements with a lumped mass matrix, and compare that to Abaqus explicit. Or if you use hex20 elements make sure you use a consistent mass matrix in MOOSE, because this is what Abaqus will use. We need to get a nearly exact match for either of these two cases, otherwise, we have a deeper problem here.

[Mriganabh]

Hi Chris,

Please bear with me.

I apologize for not being very explanative in the last message. I am not sure if you had a chance to go through the entire conversation between me & Chandu. If not, I highly recommend doing so. That way you should be able to understand the entire background.

That being said, I will address your queries individually;

1. I am that we have to use "order=SECOND" for all variables & aux-variables when using HEX20. I have used them wherever it is necessary.

2. I am modeling a cantilever beam fixed in x, y & z at the base & subjected it to a compressive pressure of 1 kip/ft^2 (see Fig-1). In Mastodon, I requested the stress & displacement time-history at particular points (namely 0, 0, 10 & 0, 0, 20). In ABAQUS,  I use the stress-history from one of the integration points closest to physical points, since all of them identical stress-history, & displacement-history of a node at the same elevation since I am concerned about Disp-z only. The oscillations observed in the stress-history when using HEX20 elements are probably due to over-deformation of the element along the z-direction which leads to the stress overshooting ( > 1 kip/ft^2) initially and then element trying to come back to its steady-state which leads to under-predicting the stress. This process keeps repeating itself since there is no damping in the system. This is analogous to a flexible spring loaded all of sudden. We do not see such behavior in the case of HEX8 elements since they are stiffer than HEX20 elements.

Figure-1

3. HEX8 elements - I am comparing the results from ABAQUS/Explicit with Central Difference time integration in MASTODON using Lumped & Consistent Mass Matrix. Both ABAQUS/Explicit and MASTODON (Central Difference with Lumped Mass Matrix) use direct lumping, see previous messages for clarification. Inherently, we expect results from using Central Difference with Consistent Mass Matrix to not match well with ABAQUS, which can be seen in the plots. However, we also observe discrepancies between the ABAQUS/Explicit & MASTODON (Lumped) which was not expected. (First 3 graphs in the PDF)

   HEX20 elements - ABAQUS/Explicit does the support HEX20 elements. Hence, I am comparing results from ABAQUS/Standard with Implicit & Central Difference Time Integration in MASTODON using Consistent Mass Matrix. Since all of them use consistent mass matrices, they seem to match pretty well (Last 3 graphs in the PDF)

4. I have attached the necessary input files.

Let me know if you have any questions.

Thanks,

Mriganabh

On Monday, February 17, 2020 at 5:50:35 PM UTC-5, Mriganabh wrote:

[Christopher Wong]

Mriganabh,

I see now that you are using `order = SECOND` with your HEX20 elements, this is good. I still don't understand why there are oscillations for a static pressure load, but I will have to actually run your models. 

To be clear MASTODON + HEX8 + CDM + LUMPED = ABAQUS + EXPLICIT + HEX8, and MASTODON + HEX20 + CDM + CONSISTENT = ABAQUS + STANDARD + HEX20, are these combinations correct? I guess I'm not sure what the problem is here (if any). If your goal is to compare MASTODON to Abaqus, then these two comparisons are the only ones that matter.

[Mriganabh]

Chris,

Yes. That's right. These two are the only ones that matter.  

[Chandu Bolisetti]

Hi Mriganabh, 

Sorry for the late response. I am not sure why there are differences in the results either. I'll have to look at the mastodon simulation more closely. A couple of suggestions if you are looking into this: 

1. As Chris mentioned please make sure that there is a full equivalency between the two models - type of elements, type of integration (try full integration), mass matrix type, damping formulation, etc. 
2. I see that you used the implicit=false parameter in all blocks. You only need to do this in the strain block. This may not be an issue, but I haven't tried using implicit=false in all blocks. 
3. I suggest you input a displacement instead of pressure using a FunctionDirichletBC. We haven't looked into the compatibility of the PressureBC with explicit yet. 
4. Try doing this for a single element first. I suggest starting here. The lumped mass problems here have been verified by comparing with equivalent problems where the mass is manually lumped using nodal masses. The input files for all of them are included in that folder. Ideally, the MASTODON and ABAQUS results should be almost identical for a simple problem like this. 

Thanks for willing to create an example -- we always welcome these contributions. Here's what you need to add for an example: 

1. Example input files in mastodon/examples/ex** 
2. A .md file that describes the example in mastodon/doc/content/examples/example**.md
3. Also, add this example to the list in mastodon/doc/content/examples/index.md
4. After creating these files commit them and create a pull request. 
5. We will then review the pull request, make changes if needed and merge it. 

I do think we need to resolve the differences between ABAQUS and MASTODON before publishing the example. 

Please let us know if you need help while doing this. 

--

Chandu

[Mriganabh]

Hi Chandu,

Thank you for the information. I will start working on the example.

I tried making sure that there are no discrepancies between ABAQUS & MASTODON models which include element type, Mass matrix formulation, integration scheme, and damping formulation. According to me, there are three takeaways - 

1. MASTODON + IMPLICIT  &  MASTODON + EXPLICIT match pretty well. I can add that to the example. 

2. ABAQUS + STANDARD + HEX20 + CONSISTENT   &   MASTODON + EXP + HEX20 + CONSISTENT also match well.

3. ABAQUS + EXP + HEX8 + LUMPED   &   MASTODON + EXP + HEX8 + LUMPED have discrepancies. In ABAQUS/Explicit, the parameters "Linear and Quadratic Bulk Viscosity" are not considered part of the material's constitutive response. They introduce damping associated with volumetric straining. I had set them to 0 since there is no damping in my MASTODON model. I am not sure but these might be causing the discrepancies.

Let me know if you have any questions.

Thanks,

Mriganabh

[Chandrakanth Bolisetti]

Mriganabh,

 

Good to know that #1 and #2 match well. We need to look into #3 in more detail. But yes, please feel free to create an example for #1 and #2.

 

--

Best regards,

Chandu

 

From: mastodon-users <mastodo...@googlegroups.com> on behalf of Mriganabh <mrigan...@gmail.com>
Date: Friday, July 10, 2020 at 2:59 PM
To: mastodon-users <mastodo...@googlegroups.com>
Subject: Re: [EXTERNAL] [mastodon-users] Re: Explicit Time Integration in MASTODON

 

Hi Chandu,

 

Thank you for the information. I will start working on the example.

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