Material Jacobian in UMAT

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Hello,

I‘m trying to write a UMAT Subroutine for an isotropic NEO-HOOKE Material (compressible, hyperelastic). I‘ve found the paper „Writing User-Subroutines“ from the forum.

The paper gives me the fourth order tensor of the Material Jacobian C(4) (DDSDDE) specified for a NEO-HOOKE Material with respect to the deviatoric left Cauchy Green tensor Bdev. Now I‘m trying to understand how they derive the Material Jacobian C(4):

• Is there a formular to derive C(4) with respect to the deviatoric left Cauchy Green tensor Bdev? (I only find formulas with respect to the right Cauchy Green tensor C)?

• Does anybody have the calculation of C(4) with the steps of the calculation?

• What kind of Material Jacobian do they use (C(4)? C(4)iso? C(4)dev?...)?

• Why is the deformation gradient F symmetric in the UMAT-Code?

I‘ve searched the whole ABAQUS Documentation and a lot of Literature (Holzapfel, ….) but can‘t find answers to my questions.

I hope anybody can help me.

Thanks

Christof