# OGDEN, N=2 and N=3 Material Model **URL:** \ **Category:** Uncategorized\ **Created:** [March 27, 2023, 11:24am UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563 "2023-03-27T11:24:51Z")\ **Posts on this page:** 10\ **Page:** 2
**Author:** ![JuanP74](https://avatars.discourse-cdn.com/v4/letter/j/b5a626/32.png) [@JuanP74](https://calculix.discourse.group/u/JuanP74)\ **Post date:** [May 16, 2023, 6:13pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/21 "2023-05-16T18:13:29Z")
It looks like both are the same model with different constants, the issue is that these models are approximations to compressible behaviour but have to be considered almost incompressible.[Ogden Hyperelastic Model for Nonlinear Finite Element Analysis | by WELSIM - Engineering Simulation Software | Medium](https://getwelsim.medium.com/ogden-hyperelastic-model-for-nonlinear-finite-element-analysis-df9518de3b48) ---
**Author:** ![JuanP74](https://avatars.discourse-cdn.com/v4/letter/j/b5a626/32.png) [@JuanP74](https://calculix.discourse.group/u/JuanP74)\ **Post date:** [May 16, 2023, 6:15pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/22 "2023-05-16T18:15:18Z")
Ogden conditions look mandatory for strictly incompressible models but maybe can be relaxed for compressible materials (however an approximation to almost incompressible materials). ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [May 16, 2023, 7:47pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/23 "2023-05-16T19:47:30Z")
Yes. In fact, this post was motivated by a high value of the Jacobian. I guess I need to track it to see how far I can go. I have just realize this verification file has the same constants I was using so it should be fast to extract the values a plot. ---
**Author:** ![JuanP74](https://avatars.discourse-cdn.com/v4/letter/j/b5a626/32.png) [@JuanP74](https://calculix.discourse.group/u/JuanP74)\ **Post date:** [May 16, 2023, 8:31pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/24 "2023-05-16T20:31:18Z")
but did you take into account this limitation? ![Captura de pantalla 2023-05-16 a las 22.25.58](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/d/d61cfb451a4d87c64a082f8462d309e06ba1a3a8.png) CCX finite element formulation cannot solve incompressible materials so there is a limit to the values _Di_ 's can accept. ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [May 16, 2023, 8:46pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/25 "2023-05-16T20:46:53Z")
Yes. I also discovered (not really me, Victor and Calc\_em ) that going too far with D1 and D2 can trigger ccx to automatically consider a minimum value of compressibility, so I have to set up as low as possible but carefully. EDITED: Much better this time. 🤣. I think Abaqus struggles with incompressibility too up to a certain point because the verification doesn’t impose the same strain ratio to all the stress states. (They know biaxial is more fragile. I think I understan better the picture. ) Let’s see how it ends up. ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/3/3a5bc7f68b1849262a097fe1f621fd90fcdde8aa.png) ---
**Author:** ![JuanP74](https://avatars.discourse-cdn.com/v4/letter/j/b5a626/32.png) [@JuanP74](https://calculix.discourse.group/u/JuanP74)\ **Post date:** [May 17, 2023, 1:48pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/26 "2023-05-17T13:48:43Z")
Ogden’s original formulation is not the same as Abaqus/CCX so if I do the conversion with this example I get mu\_Og\_1=160, alpha1=2, mu\_Og\_2=-40, alpha2=-2, that fits original Ogden’s criteria, using this formula ![Captura de pantalla 2023-05-16 a las 16.26.43](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/8/892c763a99a2f6f2bc48d05c9244ec2c35f5e313.png) my remark was done before I checked that there are 2 different formulations. ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [May 17, 2023, 6:12pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/27 "2023-05-17T18:12:43Z")
Nice. I think this check could be incorporated into ccx and send a warning in case it’s not fulfilled. Ogden is not responding as expected. Those parameters do not fit the Treloar Experimental data as Arruda did not even close. There is a very big difference and I’m considering various options. -Ogden N2 is unable to capture that behavior and that is not a good verification example. -I’m not reading those parameters properly (I don’t understand why manual says units are not important just for that model¿?¿?). I have also considered they are expressed in the same units as Treloar results (Kgf/cm2) but …no. -There is some issue with the Ogden material model as Abaqus verification file says there is good agreement. Has someone else try those coefficients?. They don’t fit the curves to me. I have work on Neo Hook and Mooney Rivlin too. Waiting for response but at first sight seems there is an excellent agreement. ---
**Author:** ![JuanP74](https://avatars.discourse-cdn.com/v4/letter/j/b5a626/32.png) [@JuanP74](https://calculix.discourse.group/u/JuanP74)\ **Post date:** [May 17, 2023, 7:21pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/28 "2023-05-17T19:21:31Z")
Ogden himself in his original paper fitted Treloar experimental data (WARNING: coefficients are those of Ogden’s original formulation, not the one in CCX/ABQ) ![Captura de pantalla 2023-05-17 a las 21.17.58](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/7/78346de843773c54d79ec49bbfd1a1b5ba7a6acc.png) I haven’t checked if data in Abaqus manual is equivalent to that in Ogden1972 but looks like it is not… ---
**Author:** ![JuanP74](https://avatars.discourse-cdn.com/v4/letter/j/b5a626/32.png) [@JuanP74](https://calculix.discourse.group/u/JuanP74)\ **Post date:** [May 17, 2023, 7:58pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/29 "2023-05-17T19:58:33Z")
I have checked the conversion with CCX formulation from data in the paper and get same results using mu1=8.8277 [MPa] , alpha1=-4.2883, D1=0.001 so looks OK (original data used original Ogden’s model with mu1=-4.1171, alpha1=-4.2883, incompressible). I haven’t checked yet biaxial, planar, volumetric… ![Captura de pantalla 2023-05-17 215224](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/a/a4ffec8bf3252b4d0a4bb07087ad63aa2c56f2e7.png) ---
**Author:** ![Disla](https://yyz2.discourse-cdn.com/free1/user_avatar/calculix.discourse.group/disla/32/3548_2.png) [@Disla](https://calculix.discourse.group/u/Disla)\ **Post date:** [May 17, 2023, 9:25pm UTC](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563/30 "2023-05-17T21:25:06Z")
The coeficients sugested in the Abaqus webpage looks completely wrong. The ones published in the Ogden original work fits much better once transformed. Incompressivility keeps low with Jacobian maximum value = 1.007 đź‘Ś Thank you very much Juan. ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/e/ee222f6986c7a7167f63c774dbbc8fe87523e27a.png) ![imagen](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/8/886b3e57d7944c03c848b7255d344a903abac1ce.png) [Previous page](https://calculix.discourse.group/t/ogden-n-2-and-n-3-material-model/1563.md?page=1)