# Input variables used in Abaqus UMAT: STRAN, STRESS and DSTRAN

I wonder the mathematical expressions for the variables: STRAN, STRESS, and DSTRAN which are used in UMAT.

According to Abaqus manual, STRAN is "An array containing the total strains at the beginning of the increment. ... In finite-strain problems the strain components have been rotated to account for rigid body motion in the increment before UMAT is called and are approximations to logarithmic strain." I do not know what the 'strain' is (Green-Lagrangian strain?) and how strain components are rotated mathematically. And by the way why is it an approxiamation to logarithmic strain?

The same question applies to STRESS variable since it is written in Abaqus manual as "in finite-strain problems the stress tensor has already been rotated to account for rigid body motion in the increment before UMAT is called, so that only the corotational part of the stress integration should be done in UMAT. The measure of stress used is “true” (Cauchy) stress."  I am confused by the 'rotation' and 'corotational part'. I wonder how this STRESS is exactly related to Cauchy/the first PK stress/the second PK stress.

Finally, I wonder if DSTRAN = STRAN_{n+1} - STRAN_{n}.
Thanks!

### Yes that is true

If you find it confusing use the large displacemnts by turing NLGEOM = yes in input file and then use the deformation gradient

DFGRD1 and calculate the finite strain E= (F'F-1)/2.0 and then calculate the stress. if you so it this way you will find that in finite strains or large displacements the strain (STRAN) is the log strain and without any rigid rotations and the stress calculated is cauchy stress.

I hope this clears your doubts.  I also noticed this in the starting but after this small exercise things became clear.