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Deformation gradient in VUMAT of ABAQUS

Dear All,

     In ABAQUS manual, it is said for hyperelastic material, it is better to define it by stretch tensor U. But if I need to use deformation gradient F in the material model directly, I need to rotate the stress back to corotational frame. How should I do that?  Should I make a polar decomposition of F=R*U first, and then apply Rt*S*R? or I can use the relative spin increment already provided to do that? If so, how?

     Also, an alternative method I think is that I can rotate the deformation gradient to corotational frame  first, and then calculate the stress based on tranformed deformation gradient. Is that right?

     In ABAQUS manual, it is said all stress and stretch tensor are defined in corotational frame, but how about deformation gradient? which frame is it defined in?

    Thank you very much.

Best wishes,


Hi Zhangli,

The deformation gradient F is already provided  by ABAQUS and you can directly use it in UMAT programming. I think the rotation and stretch tensor is also provided.  Since you are using Hyperelastic hypothesis, you should define your own configuration using UMAT. ABAQUS provides a utility routine ROTSIG to rotate the stress or stress like tensor such as back stress, etc.., but maybe that utility routine is based on Hypoelastic decomposition. Please refer to ABAQUS manual and I hope you can get some ideas. Good luck.



Xiaoteng Wang


Rotation tensor is not provided in VUMAT, and I think polar decomposition of F is still required.

Also ROTSIG is for ABAQUS Stand. I am using VUMAT (Explicit).




Hi Zhangli,

Sorry I missed the V when I read your VUMAT thread.:)

Anyway I think you can achieve the decomposition of F. VUMAT provides the stretch tensors at both current step and previous step.

Another thing is the deformation gradient is objective (rotation free), so you dont need to rotate it.



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