# Second derivative of right cauchy-green tensor in freefem

**URL:** <https://community.freefem.org/t/second-derivative-of-right-cauchy-green-tensor-in-freefem/2355>\
**Category:** General Discussion\
**Created:** [March 24, 2023, 12:12am UTC](https://community.freefem.org/t/second-derivative-of-right-cauchy-green-tensor-in-freefem/2355 "2023-03-24T00:12:28Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![yhao](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@yhao](https://community.freefem.org/u/yhao)\
**Post date:** [March 24, 2023, 12:12am UTC](https://community.freefem.org/t/second-derivative-of-right-cauchy-green-tensor-in-freefem/2355/1 "2023-03-24T00:12:28Z")

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Dear All,

I am working on 3D compressible neo-hookean solid with Freefem. I searched and got this 2D example from the forum (from [Simulating neo-hookean material](https://community.freefem.org/t/simulating-neo-hookean-material/1480)) and here is the code provided:  
[ElasticLaw2d.idp](https://community.freefem.org/uploads/short-url/sj8LfupIMZZB3gOpIFc6F4g9w1j.idp) (2.9 KB)

I am trying to extend the code to 3D. I have managed to derive the first order derivative `dC2` in the example code however I meet difficulty when trying to derive the second order derivative ‘ddC2’ in the example code. My hand-derivation leads to a different result. Could you maybe point me to any derivation process of the expression?

Thank you in advance!

Best wishes  
Yue