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

From: Igor Peterlik
Subject: [Getfem-users] Mooney-Rivlin and negative material constants
Date: Thu, 31 May 2007 11:30:30 +0200

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, 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 (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?



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