I am simulating arc welding where, my initially I perform a non-linear transient thermal analysis and then I do a non-linear elasto-plastic analysis under thermal loads.
During thermal analysis, full Newton-Raphson method converges successfully at all times (i.e heat source starting, moving, stopping and post stopping).
However, during the quasi static elasto-plastic analysis, the full newton raphson method is unable to converge the solution when the material starts to cool after welding. (i.e when, temperatures at all the nodes of the model start to monotonically decrease).
Can anyone provide some expert insights into this matter. Thanks
https://www.epsilonfea.com/wp-content/uploads/2015/05/epsilon_convergence.pdf
Check this document that may be helpful.
According to my experience, you may
1 check the error(s) in your model, e.g. check if there is any rigid body motion
2 use smaller elements in the critical region
https://www.padtinc.com/blog/ansys-mechanical-overcoming-convergence-difficulties-with-automatic-remeshing-nonlinear-adaptive-region/
https://www.youtube.com/watch?v=jnJad8BoqZg
3 define more substeps
Thank you sir for you expert insights. I would look into my model for these possible changes.
Which FEM software are you using for your simulation?
Anyway, you might have to reset the convergence criteria in your model and check
What convergence criteria are you using currently, and how did you get that?
Shekhar Srivastava sir, I am not using any commercial FEA software as of now. The analysis is being performed in MATLAB.
I have checked both residual force convergence criteria and residual energy convergence criteria, they give the same errors.
The non-convergence of full Newton-Raphson during the thermo-elasto-plastic FEA analysis starts when the heat source is removed at the weld end time. I reduced step size at these instants, but found no improvement.
The major observation which I had found was that the incremental displacements at end-weld-pool start to 'oscillate' or 'diverge from zero', when the heat source is removed. Any insights would be helpful in this regard.
In my simulation, I am using small displacement theory, assumed no phase transformation plasticity, assumed J2 plasticity theory with very small amount of hardening.
There is no guarantee that N-R or any other method of solving one or more nonlinear equations will ever converge. With a reasonable starting value and a smart implementation with checks and restarting will often yield the desired result, but that's not a given. Many nonlinear equations have multiple solutions, which may be local minima when you are seeking a global minimum. This is why it is helpful to have full control over the calculations. Building a task inside MATLAB and depending on the algorithms provided may often work, but this is not always the case, as in your present example. This is one of many reasons why I would never use MATLAB to do anything. If you're stuck with MATLAB and have no other options, I suggest you try other methods, including: Regula-Falsi, Secant Method, Davidon-Fletcher-Powel, Broyden, and evolutionary, to name a few.
Thank you Dudley J Benton Sir, for your useful insights.
I would look into the possibility of using other solution methods apart from Newton-Raphson.
Which software are you using? I would make sure CTE is defined for the temperature range you are trying to evaluate, and avoid any extrapolation being done by the software.
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