Yeoh 2nd and 3rd order

[zawada98]

In this PR, I have implemented the 2nd and 3rd Yeoh material models, whose strain energy density function reads:

W = C1 (I1-3) + C_2 (I1-3)^2 + 0.5K_1 log(J)^2 + 0.5K_2 log(J)^4
W = C1 (I1-3) + C_2 (I1-3)^2 + C_3 (I_1-3)^3 + 0.5K_1 log(J)^2 + 0.5K_2 log(J)^4 + 0.5*K_3 log(J)^6

I1: First material invariant
J: determinant of the deformation gradient tensor and is also = volumetric change in object

\Kappa_i : ith compressibility factor. As you can see here, the number of compressibility factors = order of the model. This is standard practice in commercial FEA simulation tools and allows for more flexibility when characterizing the material.

The following material constants can be used for testing:

3rd order: C1 = 0.57382 MPa, C2 = -7.4744E-2 MPa, and C3 = 1.1321E-2 MPa
K_1 = 200 MPa, K_2 = 20 MPa, K_3 = 4 MPa

Sources:
[Accessed 3rd of February 2026]
https://welsim.com/2021/05/25/yeoh-hyperelastic-model-for-nonlinear-finite-element-analysis.html
Note: in this reference the bulk part (i.e. K_i log(J)^2 for us) is modeled using the "D_i" constant which is = 2/K_i

[alxbilger]

You must add those files to the CMakeLists.txt file, otherwise they are not compiled.

[zawada98]

added

[alxbilger]

Hey @zawada98,

I fixed the code and introduced an example scene. However, the simulation explodes. I believe that I have all units consistent with the SI. What do you think?