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# Problem with fortran code for solving large strain 2D elastic problem by FEM using Updated Lagrangian Framework

I am using my own fortran code to solve a large strain 2D elastic problem using FEM in Updated Lagrangian framework and I am using incremental formulation. It works well for 2D pull of a square block with 2 elements and I've compared the results with a commercial FEA package. But while solving bending of a cantilever beam the results starts to blow up and the elements distort abruptly after certain time step. This happens only when the load or the displacement given at the free end of the beam is large otherwise it works fine.

Basically, I am supposed to solve a gradient visco-plasticity problem using the formulation given by Niordson and Fleck (see the paper attached herewith). I am facing the same problem when using the viscoplastic formulation. The results start to blow up after few steps only.

Does anyone have any idea what could be the possible problem?

Attachment | Size |
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Gradient Viscoplastic.pdf | 302.94 KB |

## time-step estimation?

Are you sure your time-step estimation is correct?

## I hope so. I am using quite

I hope so. I am using quite small time step but not sure. The bending problem of a simply supported beam with a concentrated load at mid span works well also.

Suman Guha

Ph.D Student

IIT Kanpur

India

## element type

If you succeeded in simulating simple tension test, I suggest you to simulate simple shear test. In a first guess, the 2D continuum element (not beam element) is not appropriate for the bending problem. Also, you can check the part of implementation on using objective stress rate from simple shear test. Long time ago, I implemented large elaso-plastic deformation problem based on the convective Lagrangian framework (same formulation of your attached paper). It is very hard task for me. Good luck.

## Thanks for your reply. I'll

Thanks for your reply. I'll try to do the simple shear test. I'm using 6-noded plane strain triangular element for the simulation.

## reestimating timestep

> This happens only when the load or the displacement given at the free end of the beam is large otherwise it works fine.

Since you mentioned this, are you reestimating your time-step after every time-increment?

-Nachiket

## No I am using constat

No I am using constat time-step.

## Wave-speed changes

Wave speed changes with stiffness which changes with strain. This may cause the critical time-step to drop. Perhaps this could be an issue.

## Reply to Suman

Suman,

The paper is not found attached.

Do you have documentation for your code, consisting of both: (i) the documentation for code and (ii) a brief technical document containing the mathematical FE model being implemented (in detail---not as in a research paper)? If yes, if you send me the documentation together with the code, I will be able to locate the problem.

Also, I don't quite understand why you quote the 2D square block with 2 elements. Does it have anything to do with your code for the beam (apart from serving as a small test for time-stepping)? ... Just a shot in the dark, this is. But if you send the above, I can look into it on a weekend.

--Ajit

## Thanks for your reply Dr.

Thanks for your reply Dr. Jadhav. Sorry that the paper was not attached last time. Please find it now in the original post.

Thanks

Suman