# Strain Energy density Neo Hookean / Mooney Rivlin

**URL:** <https://calculix.discourse.group/t/strain-energy-density-neo-hookean-mooney-rivlin/1686>\
**Category:** Uncategorized\
**Created:** [May 31, 2023, 8:45am UTC](https://calculix.discourse.group/t/strain-energy-density-neo-hookean-mooney-rivlin/1686 "2023-05-31T08:45:33Z")\
**Posts on this page:** 5\
**Page:** 1

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**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 31, 2023, 8:45am UTC](https://calculix.discourse.group/t/strain-energy-density-neo-hookean-mooney-rivlin/1686/1 "2023-05-31T08:45:34Z")

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Hi,

I need some help.  
I think there is a possible error in the Strain Energy density computation for Neo Hookean / Mooney Rivlin hyperelastic material models (probably extends to Polynomial too ).

Analytical solution= 0.525 MPa  
Result = 0.79 MPa

Nominal stress and Strain curves agree with expected solution but not the final Strain Energy density.  
This is an Hyperelastic model and strain energy density is a potential (I would expect solution only depends on final stretch lambda\_u and C10 coefficient).

> **[Hyperelastic Neo Hookean Mooney-Rivlin Strain Energy .pdf](https://wetransfer.com/downloads/5c752d04efc3c04e97ecb03865ca91de20230531083839/97685d)**
>
> 1 file sent via WeTransfer, the simplest way to send your files around the world

```auto
** Generated by Mecway 19.0
*NODE
1,0,0,0.1
2,0,0,0
3,1,0,0.1
4,1,0,0
5,0,-0.1,0.1
6,1,-0.1,0
7,0,-0.1,0
8,1,-0.1,0.1
*ELEMENT,TYPE=C3D8
1,6,8,3,4,7,5,1,2
*ELSET,ELSET=Hexahedral
1
*SURFACE,NAME=Moving_face
1,S1
*SURFACE,NAME=Base
1,S2
*MATERIAL,NAME=Neo_Hook
*HYPERELASTIC,NEO HOOKE
900000,2E-10
*MATERIAL,NAME=Mooney_Rivlin
*HYPERELASTIC,MOONEY-RIVLIN
900000,0,2E-10
*SOLID SECTION,ELSET=Hexahedral,MATERIAL=Mooney_Rivlin
*BOUNDARY
1,1,,0
1,2,,0
2,1,,0
2,2,,0
2,3,,0
3,2,,0
4,2,,0
4,3,,0
5,1,,0
6,3,,0
7,1,,0
7,3,,0
*AMPLITUDE,NAME=A_1
0,0
500,-0.5
*TIME POINTS,NAME=timepointsname
1
*STEP,NLGEOM=YES,INC=110,AMPLITUDE=STEP
*STATIC
5,500,0,5
*BOUNDARY,AMPLITUDE=A_1
3,1,,-1
*BOUNDARY,AMPLITUDE=A_1
4,1,,-1
*BOUNDARY,AMPLITUDE=A_1
6,1,,-1
*BOUNDARY,AMPLITUDE=A_1
8,1,,-1
*NODE FILE,GLOBAL=YES,TIME POINTS=timepointsname
U,RF
*EL FILE,TIME POINTS=timepointsname
S,NOE,ENER,E
*EL FILE 
ENER

*EL PRINT, ELSET=Hexahedral
ENER
*END STEP

```

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<div class="post-metadata">

**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\
**Post date:** [May 31, 2023, 2:22pm UTC](https://calculix.discourse.group/t/strain-energy-density-neo-hookean-mooney-rivlin/1686/2 "2023-05-31T14:22:14Z")

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In Abaqus, I got 0.5249 MPa:

 ![strain energy density](https://global.discourse-cdn.com/free1/uploads/calculix/original/2X/2/20c6fc197871c8a5e12a4550b7a91dd2c71f67b0.png)

The raw result is in J/m^3.

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<div class="post-metadata">

**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 31, 2023, 4:32pm UTC](https://calculix.discourse.group/t/strain-energy-density-neo-hookean-mooney-rivlin/1686/3 "2023-05-31T16:32:06Z")

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Thanks Calc-em.

I think Mr. Guido Dhondt follows the site ¿isn’t it?  
¿Do you think it’s needed to post the issue in the GitHub too.?

Regards

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<div class="post-metadata">

**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\
**Post date:** [May 31, 2023, 4:37pm UTC](https://calculix.discourse.group/t/strain-energy-density-neo-hookean-mooney-rivlin/1686/4 "2023-05-31T16:37:09Z")

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Yes, let’s notify him: @dhondt

But GitHub issue is definitely a good idea too.

---

<div class="post-metadata">

**Author:** ![Calc\_em](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Calc\_em](https://calculix.discourse.group/u/Calc_em)\
**Post date:** [August 1, 2023, 9:59am UTC](https://calculix.discourse.group/t/strain-energy-density-neo-hookean-mooney-rivlin/1686/5 "2023-08-01T09:59:38Z")

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This bug is fixed in CalculiX 2.21.