SymbolicEnergy for MixedProblems

Hello there,

I wanted to ask, whether it's possible to define a SymbolicEnergy for solving an almost incompressible nonlinear elasticity problem. For that I would like to try out a penalized energy function of the type

Psi(C,p) = Integrate(NeoHooke(C) + p * Theta(J) - 1/2*kappa * p^2)

where C = F^T . F (like in the elasticity demo in the docs), J = sqrt(det(C)), Theta(J) = Log(J).

If i do the directional derivatives wrt p i get the side constraint
Integrate((Theta(J) - 1/kappa * p)*q) = 0

Can I do this in NGSolve?

Cheers
Elias

Hi Elias,

yes, with SymbolicEnergy you can define also a Lagrangean, and NGSolve computes first and second variations for you.

A big question is what are good finite element pairings. We are currently working on stable mixed formulations for hyperelasticity in H(curl) and H(div), the preprint should be available in a month.

Best,
Joachim

Thanks for the Answer. You wouldn't happen to have a working minimal example?

Cheers
Elias