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


From: Yves Renard
Subject: Re: [Getfem-users] Mooney-Rivlin and negative material constants
Date: Mon, 4 Jun 2007 12:36:44 +0200
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Le jeudi 31 mai 2007 11:30, Igor Peterlik a écrit :
> 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.

Indeed, i am not an expert in  Mooney-Rivlin material  constants.
It may be understandable that if the constant C_01 is to much negative, the 
poly-convexity of the law could be lost (but really, I did not study this at 
all). Are you sure the values you obtained are in an acceptable range ?

The constants in the Getfem brick are defined as follows (strain energy) :

W = C_01 ( I_1(C) - 3) + C_10 (I_2(C) - 3)

where $C  = (\nabla \phi)^T \nabla \phi$ is the right Cauchy Green tensor and
I_1, I_2 the two first usual invariants. Is it the definition you expected ? 


Yves.

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  Yves Renard (address@hidden)       tel : (33) 04.72.43.80.11
  Pole de Mathematiques, INSA de Lyon          fax : (33) 04.72.43.85.29
  Institut Camille Jordan - CNRS UMR 5208
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