Simutalion of neo-hookean material with MPM and FEM

Dear all,

I am new to Taichi and am trying to simulate beam bending both with MPM (Material Point Method), using Taichi, and FEM (Finite Element Method, using FreeFem++, Compressible Neo-Hookean materials).

I use neo-hookean material as described in the FreeFem++ example, after adding a second term to the energy W related to lambda, the second Lamé coefficient, as described in Wikipedia Neo-Hookean_solid.

I find two different final configurations for the beam with MPM and FEM (see picture attached in the notebook) and cannot figure out why. The two methods are supposed to modelize correctly neo-hookean materials.

I am wondering whether anybody ever did this same exercise and the result you found.

This is the link to the gist including the codes for MPM and FEM along with the notebook producing the plot of the two final configurations:

Thank you very much for any clue!


Hi @djamel ,
Welcome to Taichi community!
It seems that the beam simulated by the FEM is harder than that of MPM. I suspect that the simulation resolution of FEM is not high enough comparing to the MPM. Would you mind improving the resolution of the mesh for the FEM and give any other try? Thanks.

Another thing to try: the uses fixed-corotated material mode. For engineering problems, you may want to use the real Neo-Hookean model.

Here is a Neo-Hookean example in 3D:

(Ignore L143 since that is for the internal actuation force in the soft robot.)

One thing you can try is to replace the material model in with Neo-Hookean, so that both MPM and FEM use the same material model.

(Actually, for relatively small deformations, material models should not have such a big impact on the simulation results - but at least unifying the material models help remove one potential cause of inconsistency.)