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Coupling FEM and Monte Carlo

I want simulat micro strucure evolution in metal fromind, e.g. rolling. To capture grain growth or refinement, i use MC method and rolling process simulate by FEM method (ABAQUS). Do any one have experience in this field?


bitamendi's picture

Hi!I don't understand very well. You want to use a MC method, to define the initial state of the FEM simulation? Or you want to link the MC method with the FEM to use it at every increment?

Thanks for your attention. I want to link FEM and MC in every step.

bitamendi's picture



Sorry ,


when you  say at each step, is at
the bigining of an Static or dynamic step like:



1, -12.875431,
0.035724, 0.133323








Or you want to say
at each increment of one step (understanding step as
above), link abaqus with MC.

If you want the
first option (between steps), you can do it working with the .inp, you can
start with an .inp make an step,  and at
the end of the step read the results, do the MC and rewrite the next step’s


On the other
hand, if you want to link the MC at each increment, I think that you have to
use subroutines, for that you have to know where will you modify the normal
abaqus rutines with the MC, e.g., if you want to move the nodes you have to use
USEMOTION, if you want to work with the material parameter field subroutine, or

I don’t know if
you are understanding me (I know that my English is not terrible…)

I’m not sure if
I will be able to help you, but if I don’t answering you here send me an e-mail

Thnks agin for your help. Important problem in my quastion is about physics of process. In cold rolling ( ofcourse ARB ) graine size is closed to 100-200 nm that cause deformation mechanism drastical changed. My goal is study of grain refinement in metal deformatin. I known that MC method is used for recrystalization in aneanlling.Do i can use MC method for grain refinemn under straint ?

bitamendi's picture

Sorry again,

I think that our misunderstanding
came from that I’m not familiarized with those MC techniques, sorry about that.

If I understood that I went
to read in the web about it, tell me if I’m wrong please. The MC technique is
used to forecast the recrystallization structure and texture evolution, in your
case you are concerned about the grain refinement.

My question is:

*In the “n” state, you have
a specific configuration: number of elements, node positions, material behavior…
and then you want to use the MC method in order to forecast the grind
refinement. But, what implies this grind refinement? Some change in material behavior?
Material behavior’s constants change? The nodes change their position? You have
to recreate the mesh?

For each case you have to
use a different user subroutine, in those subroutines (which are executed at
each increment) you have access to the “n” state information, and I think that
is there where you can implement your MC method to update the “n+1” state
taking into account the grind refinement.

Bur before you have to
define what changes implies that grind refinement.

Ofcourse my explation was short.

In MC (Potts model) grain boundary move as system energy is reduced. In my case grain crystallographic orientation , temperture and strain (or stress) distribution as result of metal deformation are depended variable of system energy ( that must reduced in every step). In papers that i saw temperture and crystallographic orientation are implemented but i didn't see work that implemented strain distribution in every step. In plastic deformation effect of grains in structure are studied with crystal plastic FEM or texture component crystal plastic FEM (as i searched). deformation mechanisms in poly crystal materials  is resulted from strain hardening that come from dislocation movement ( and other mechanism e.i. twining). Do exact behaviour grain evolution can be captured by MC methods as CPFEM or TCCPFEM?


bitamendi's picture

As far as I’m
understanding, you have already found papers that have implemented crystallographic
orientation and temperature, but no one with the strain distribution.  That is maybe because usually the FEM is
displacement governed resolution and therefore at each increment the strains
are already predefined.
With a UMAT you have to be able to redefine everything (stresses included), except

I’m not
sure if I’m helping you, ore contrary I’m talking about things that are not in
your question line…

Thanks again, your suggestion is good,
I am studying CPFEM and this field is perfect. And i am following other work on coupling MC and FEM. And every one that worked on this field ( coupling MC and FEM) please guide me.

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