Question about the computation for some values according to F（3,3，*）

[YunfeiWang]

Dear all

        Now I do a right polar decomposition for the deformation gradient(F=RU). So I get the rotation matrix 'R' and the right stretch tensor 'U'.

I want to ask that how to get the strain(logarithmic strain) increments and rotation increment from n time to n+1 time according to f(3,3,*) ?

My question is about finite deformation and my Feap version is ver8.4

                   Thank you very much

                   Best regards

[FEAP_Admin]

If you used program/eig3.f in computing the eigenbasis for C, then you can just take the log of the eigenvalues to get the logarithmic strains:  log lambda_a = (1/2) log c_a.

[YunfeiWang]

If you used program/eig3.f in computing the eigenbasis for C, then you can just take the log of the eigenvalues to get the logarithmic strains:  log lambda_a = (1/2) log c_a.

     Thank you very much , but I already got the logarithmic strain through the right stretch tensor 'U' which solved by the right polar decomposition for the

deformation gradient. And what I want to know is how to get the strain increments and rotation increment.

On my opinion:
                 
                    Through the polar decomposition for F(3,3,1) which defines F_n+1, I can get the  rotation matrix R_n+1 and logarithmic strain tensor D_n+1(by log of stretch tensor U).

                    Through the polar decomposition for F(3,3,2) which defines F_n, I can get the  rotation matrix R_n and logarithmic strain tensor D_n(by log of stretch tensor U).

So the strain increments from n to n+1 is : D_n+1-D_n and the  rotation increment is: R_n+1-R_n.

      Could you tell me that what I thought is true?

NOTE: I want to transform the abaqus UMAT in to FEAP. But the computations of abaqus UMAT is based on strain increments DSTRAN and  rotation increment
          DROT

Thank you again

Best regards

[Prof. S. Govindjee]

The strain increments are fine as you explain.

The rotations are trickier since you really have to define what you mean by a rotation increment.  I would say that
the incremental rotation that makes sense should be something more like   R_{n+1} * R_n^T, so rotate back to the reference configuration and then rotate forward to the current.

[K.Li]

Which kind of material model are you trying to implement in FEAP? Maybe you do not even need to compute strain increments and rotation increment.

[YunfeiWang]

The strain increments are fine as you explain.

The rotations are trickier since you really have to define what you mean by a rotation increment.  I would say that
the incremental rotation that makes sense should be something more like   R_{n+1} * R_n^T, so rotate back to the reference configuration and then rotate forward to the current.

Dear Professor

     Thank your answer. It is very useful . I will try it

Best regards

[YunfeiWang]

Which kind of material model are you trying to implement in FEAP? Maybe you do not even need to compute strain increments and rotation increment.

Dear K.Li

     I want to write an UMAT about crystal elastoplasticity through referring to the UMAT about（see attachment）abaqus. It needs to compute strain increments and

rotation increment.

[K.Li]

Frankly speaking, I am not familiar with this field, but if you can specifically tell us which plasticity model you trying to implement (is it the one done by Prof Y. Huang at Harvard in 1991?), I am sure someone can point you in the right direction, also check Google scholar,

https://scholar.google.at/scholar?hl=en&as_sdt=0%2C5&as_vis=1&q=feap+crystal+elastoplasticity&btnG=

[YunfeiWang]

Frankly speaking, I am not familiar with this field, but if you can specifically tell us which plasticity model you trying to implement (is it the one done by Prof Y. Huang at Harvard in 1991?), I am sure someone can point you in the right direction, also check Google scholar,

https://scholar.google.at/scholar?hl=en&as_sdt=0%2C5&as_vis=1&q=feap+crystal+elastoplasticity&btnG=

Dear  K.Li

       Thank you very much. The information provided by you is very useful for me.

Best regards