Temperature dependent elastic modulus in Abaqus

[Michael Flanagan]

Hello
I am using Abaqus to give an insight into a problem with temperature dependent properties.
When I try to validate my models against closed form solutions the results are incorrect.

Model details
In order to investigate the issue I have created a much simplified single element model with a simplified loading scenario.The model has dimensions of .001*.001*.001 (1mm^3). The part has been given constant thermal expansion of 2.5e-5. The part has been given a temperature dependent young’s modulus of 9e9 (9Gpa) below 150C and 1e9(1Gpa) above 160C. The part has been constrained in the x direction on opposite faces and the corners of the part have been constrained in order to prevent translation and rotation. A predefined field has been applied to the whole part which cools the part linearly from 330C to 25C. This causes a thermal strain in the element which in turn causes stress.

Closed form solution details
I calculated the strain incrementally in 12 steps. The first step is from 25C-150C. The next 10 steps are from 150C-160C in 1 C steps. The next step is from 160-330. The total stress is calculated to be 3.37E7 Pa.

Abaqus solution
Abaqus gives a thermal stress of 7e7 Pa.
If I use the formula for total thermal strain in the Abaqus documentation to calculate the stress and strain I get the Abaqus answer of 7e7 Pa.

Conclusion
I have concluded that Abaqus is incorrectly using the total thermal strain instead of the incremental thermal strain in calculating the results.
I find it hard to believe that Abacus makes such a fundamental error. I suspect that I have made an error in the model and that perhaps there is an option to "switch on" incremental strain calculation that I (and my colleagues) are not aware of.
I have included an input file for the model I have used.
At the moment the only way I can see of progressing is to write a UMAT. This would be quite time consuming as I have little experience in this area and the actual material that I am using is more complex that that in the simplified model.
Has anyone come across this before or does anyone have any insight into the problem?

Thanks
Michael

 

[Mustaine3]

It is clearly documented what Abaqus is doing. If you want a different behavior, then you can use the UEXPAN subroutine.

 

[Michael Flanagan]

Hi Mustaine3,
Thanks for your response.
Your suggestion to use UEXPAN seems like a good solution.
I would like to clarify my problem before I proceed.
Can you confirm that Abaqus is using the total thermal strain and that this is incorrect when temperature dependent material properties are used?
I have used the formula for total thermal strain (from the Abaqus documentation linked below) to calculate results.

http://abaqusdoc.ucalgary.ca/v6.9/books/usb/default.htm?startat=pt05ch22s01abm51.html

This gives that same incorrect answer as Abaqus.
I have attached some details on the calculation.

Thanks

 

[Shufen]

Hey,
if you're comparing the stresss (S11,S22,S33 and so on) obtained from CAE, I think ABAQUS is giving you total stress so it is doing it correctly. With incremental strain, I think you should be checking the incremental stress. Perhaps check the ODD and subtract the stress between two successive increments.

Regards
Shufen

 

[Michael Flanagan]

Hi Shufen
Thank you for your suggestion.
I became quite frustrated with the problem and decided to park it for a while.
I will be following up with it in the coming weeks (hopefully).
I will update once I have made some progress.
Thanks
Mike

 

[Michael Flanagan]

Hi guys thanks for your input.

Re Mustaine3
I have tried using the UEXPAN code to solve my problem.
The code works fine and outputs the correct thermal strains.
The thermal strain buildup is in line with the answer given from inputting the data through CAE.
The problem with thermal stress is still occurring.

Re Shufen
I am not sure I fully understand your suggestion. I have checked the incremental stress by taking one stress value from the previous value in the ODB. This value is not correct. Is this what you are suggesting?

The issues (as I understand it) is that, although Abaqus is calculating the strain incrementally, it is multiplying the Young's modulus by the total strain to get the stress.
I still do not understand why Abaqus would do this.
I also cannot find anyone else who has encountered this error and wonder if I am making some fundamental error?
If anyone has any further input it would be appreciated.
In the meantime I will focus on writing a UMAT.

Thanks again.
Mike