Hello everybody,
My task is to write a UMAT for non-linear viscoelastic material in Abaqus. When it comes to working in 2D and 3D, I see that there are places where I have to work with 4th order tensors. I understand that stresses and strains are stored as vectors in Abaqus - UMAT and are passed in and out the same way.
- Now I don't understand how to handle the 4th order tensors accordingly.
- Should I use them as 9*9 (81 components) matrix, or use them as (3*3*3*3) matrix or how to use them as vectors suitable to work with stress and strain vectors.?
It would be nice if any of you could help me understand it or refer me to a material that might help me.
Thanks for your time
Regards
Shree
you are using Voigt notation for your stress and strain, it means you represent a 3x3 second order tensor in form of a 6x1 vector. in order to be consistent, you need to write 3x3x3x3 forth order tensor in form of 6x6 mstrix. as an example for 6 by 6 matrix, I attached a simple case of linear isotropic elastic material with constants lambda, EG (shear modulus):
NDI can be considered as number of dimensions (=3) and NTENS is dimension of matrix (=6)
DO I=1, NDI
DO J=1, NDI
E_4(I, J)=ELAM
END DO
E_4(I, I)=EG2+ELAM
! E_4(I, I)=EG+ELAM
END DO
DO I=NDI+1, NTENS
! E_4(I ,I)=EG
E_4(I ,I)=2.d0*EG
END DO
Hello Mr. Mousavi,
Firstly thanks a lot for the answer. I understand the Voigt notation. I was just not clear as to how implementation can be done in Abaqus. I have started to read more about it as well.
Regards
Shree
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