Adding MooneyRivlin to SofaCaribou
Opened this issue · 2 comments
Hi @jnbrunet , I have pushed MooneyRivlin Material file which contains strain_energy_density()
and PK2_stress()
I am pretty sure about both. But I am struggling with the PK2_stress_jacobian()
, it should return a 6x6 matrix while I am only finding a 3x3 matrix when derivating the PK2 with respect to the Cauchy tensor.
I saw that in NeoHookean you used symmetric_dyad_1()
and symmetric_dyad_2()
tensors to get this 6x6 matrix output, but am not sure to understand how you translated your PK2_stress_jacobian expression(that should be the derivative of PK2 with respect to C => An expression of C^{-1} and C^{-2}) to an expression that includes symmetric_dyad_1()
and symmetric_dyad_2()
and get the 6x6 matrix, could you please explain that ?
CC @Ziemnono
Hey @Sidaty1 ,
The derivative of a 2th order tensor w.r.t another 2th order tenser (dS/dE) is a 4th order tensor. However, in our case, this resulting tensor is symmetric and can be "reduced" to a 6x6 matrix. The details of the St-Venant-K. and Neo-Hookean materials can be find in the section 2.3 of my thesis, where I also defined these two symmetric dyad operators.