# Simulating neo-hookean material **URL:** \ **Category:** General Discussion\ **Created:** [February 8, 2022, 1:47pm UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480 "2022-02-08T13:47:07Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![djamel](https://avatars.discourse-cdn.com/v4/letter/d/76d3ee/32.png) [@djamel](https://community.freefem.org/u/djamel)\ **Post date:** [February 8, 2022, 1:47pm UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480/1 "2022-02-08T13:47:07Z")
Dear all, I am using the example given in the FF documentation about “Compressible Neo-hookean materials” in the “Mathematical Models” menu. I am wondering why the program makes use of only one Lame coefficient, mu (declared line 238). The other one, D, is declared (line 239) but never used. Thanks a lot for any clue! ---
**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\ **Post date:** [February 9, 2022, 7:02pm UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480/2 "2022-02-09T19:02:47Z")
Just to play I rebuild the test nl-elas-neo-Hooken [nl-elas-neo-Hookean-v2.edp](https://community.freefem.org/uploads/short-url/tOULDnXKQtwY4GQqZMrgMrqBePm.edp) (2.9 KB) with new set of macro [ElasticLaw2d.idp](https://community.freefem.org/uploads/short-url/sj8LfupIMZZB3gOpIFc6F4g9w1j.idp) (2.9 KB) With a clean set of Lame coefficient ---
**Author:** ![djamel](https://avatars.discourse-cdn.com/v4/letter/d/76d3ee/32.png) [@djamel](https://community.freefem.org/u/djamel)\ **Post date:** [February 9, 2022, 7:56pm UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480/3 "2022-02-09T19:56:49Z")
Thank you very much. I will try that. ---
**Author:** ![yhao](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@yhao](https://community.freefem.org/u/yhao)\ **Post date:** [April 12, 2022, 10:54am UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480/4 "2022-04-12T10:54:18Z")
Hi Frédéric, I also used this neo-Hookean mechanical model. I checked some literature and found that the neo-Hookean model with only one parameter means it is an incompressible model. So I want to make sure whether the example code given in the documentation is compressible or incompressible? Thank you! ---
**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\ **Post date:** [April 15, 2022, 12:20pm UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480/5 "2022-04-15T12:20:30Z")
I sorry I miss this message, I do not now , I am not specialists in solide mechanics ---
**Author:** ![yhao](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@yhao](https://community.freefem.org/u/yhao)\ **Post date:** [April 21, 2022, 2:29pm UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480/6 "2022-04-21T14:29:58Z")
Thank you for your reply. I will try both and see if the differences are large. ---
**Author:** ![yhao](https://avatars.discourse-cdn.com/v4/letter/y/5fc32e/32.png) [@yhao](https://community.freefem.org/u/yhao)\ **Post date:** [March 23, 2023, 10:41am UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480/7 "2023-03-23T10:41:11Z")
Hi Frederic, I am reading your script with the new macro in the .idp file. I can derive the first-order derivative of the right Cauchy-green tensor `dC2`. But when it comes to `ddC2` the second-order derivative, the expression is not very clear to me, as 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 ---
**Author:** ![cmd](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/cmd/32/67_2.png) [@cmd](https://community.freefem.org/u/cmd)\ **Post date:** [July 17, 2025, 9:01pm UTC](https://community.freefem.org/t/simulating-neo-hookean-material/1480/8 "2025-07-17T21:01:12Z")
The derivation looks correct to me. We have: C(u)=F^T(u)F(u)=(I+\nabla{}u)^T(I+\nabla{}u)=I+\nabla{}u^T+\nabla{}u+\nabla{}u^T\cdot\nabla{}u Then the first Frechet derivative is: dC(u,U)=(dF(u))^TF(U)+F^T(U)(dF(u))=\nabla{}u^T(I+\nabla{}U)+(I+\nabla{}U)^T\nabla{}u ...=\nabla{}u^T+\nabla{}u+\nabla{}u^T\cdot\nabla{}U+\nabla{}U^T\cdot\nabla{}u Then the second is: ddC(u,U)=(dF(u))^T(dF(U))+(dF^T(U))(dF(u))=(\nabla{}u)^T\nabla{}U+\nabla{}U^T\nabla{}u ...=\nabla{}u^T\cdot\nabla{}U+\nabla{}U^T\cdot\nabla{}u