[Getfem-users] Mooney-Rivlin and negative material constants

[Igor Peterlik]

Dear getfem experts,

First, thanks for providing such a great FEM code. I found 
it really useful for my research.

And now, the problem. I want to model 
a deformation of a silicon cylindric object. According to 
real lab measurements, Mooney-Rivlin material with constants 
C_10=2.94e+03 and C_01=-1.11e+03 should be suitable for 
realistic modelling of the object.

I modified and used the test program nonlinear_elastostatic.cc, setting
the EXTENSION parameter. Even for very small values of the
extension (also with large number of steps), the method
did not converge (in case it converged for really really
small extension, the result visualized in vtk looked "broken").

If I set both constants to positive numbers (absolute values 
of those given by the experimental measurement), there is no
problem with convergence, also
the visualized deformation looks 
fine, however, the results do not fit numerically the 
experimental data.

I employed linear as well as quadratic elements. I used
the Lagrangian multipliers version, as I need to compute
the reacting forces in nodes with prescribed displacement.
I also tried the other methods (penalty), the result was the
same (ok for positive, no convergence for negative).

I also tried to use the personalized solver given by Yves Renard in 
https://mail.gna.org/public/getfem-users/2006-11/msg00025.html 
(all the possibilities).
No success.

Therefore I would like to ask if there is some limitation when 
using negative values of the material constant. Is the problem 
somewhere in the model or in the solver or is there 
something wrong with the negativity of the constants?


                        Thanks


                                        Igor