What are STRAN, STRESS, and DSTRAN expressed in maths

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What are STRAN, STRESS, and DSTRAN expressed in maths

xiashank
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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 and how strain components are rotated mathematically.

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!

Andy