# 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

### Hyperelastic Material Jacobian in UMAT

Dear Christof

You can find the complete process of material Jacobian computation in the following paper:

"A FINITE ELEMENT IMPLEMENTATION OF KNOWLES STORED-ENERGY FUNCTION: THEORY, CODING AND APPLICATIONS"

You can easily google it and download it freely. Furtheremore, in case of anisotropic hyper elastic material you can use my recenty published paper. My paper link is :

http://www.sciencedirect.com/science/article/pii/S1751616115005032

Best regards.

### Dear Afallah,

Dear Afallah,

thank you very much for your support. This paper helped a lot!

Regards

Christof

### more on Neo-Hookean

Surf to
https://web.njit.edu/~sac3/Software.html
a website run by Prof. David Henann, Brown University,

and contact me privately to get a file
"A large deformation Neo–Hookean user material in ANSYS.pdf",
listing a code. I cannot find the button to upload it.

Good luck

Frank

### Thanks a lot! The papers

Thanks a lot! The papers helped to solve my problems.
best regards