Re: [Getfem-users] non linear elasticity

[jean-yves heddebaut]

Yves,

thank you very much for your help.
My problem is indeed a 2d problem.
The initial configuration is a plate, and we assume the displacements  
function of 2 variables only, the 3th dimension of the plate is  
negligible versus the other dim. (I think it could be considered as a  
plane stress problem)

I would greatly appreciate if you could send me the written info you  
are mentioning

regards

jean-yves heddebaut

Le Apr 29, 2008 à 4:56 PM, Yves Renard a écrit :

> On Monday 28 April 2008 18:39, you wrote:
> > Dear getfem users,
> >
> > I would like to  reuse the non linear elasticity brick to make a
> > brick representing the behavior of non linear membranes.
> > The idea is to apply the Cosserat hypothesis, which gives a
> > simplified Green-Lagrange strain tensor.
> >
> > The dimension of the vgrad term in the
> > asm_nonlinear_elasticity_tangent_matrix function would be (:,2,3) iso
> > (:,3,3) in the 3 dim brick, and I think I could reuse the function
> > without modification.
>
> You mean that you have a 2D problem but with a 3D displacement ?
>
> > The elasticity_nonlinear_term, on the contrary, has to be adapted,
> > but I do not see how to do it.
> > Could anybody help me understand the logic  behind the compute
> > function ?
> >
> > here is how I understand it, please tell me where I am wrong (I am
> > considering the Saint venant kirchoff hyperelastic law)
> >
> > 1.gradU is the gradient of the displacements, based on the preceding
> > iteration displacements
>
> The goal is to compute the tangent matrix and the residue, so gradU  
> is the
> gradient of the displacement of the current state (ok for preceding
> iteration).
>
> > 2.E is the Green-Lagrange strain tensor, also based on the preceding
> > iteration displacements
> ok
>
> > 3.gradU becomes gradU+I ( deformation gradient iso displacement
> > gradient ?)
> yes, it is computed because the term (Id+grad U) intervene in the  
> expression
> of weak form. this is the gradient of the deformation.
>
> > 4.tt is a tensor containing the rigidity coefficients
> Yes, for version = 0 this is the tangent terms (rigidity terms) and  
> for
> version = 1 just the term (Id+grad U) multiplied by the stress tensor.
>
> > Could somebody tell me what is done in the "version==0" loops ?
>
> This is the (ugly) computation of the whole tangent term. In  
> particular the
> multiplication of a fourth order tangent tensor given by  
> AHL.grad_sigma(E,
> tt, params). I agree that this could be simplified in practical  
> situations
> but the goal was to make a generic computation in a first time.
>
> > I would greatly appreciate any help
> >
> > jean-yves heddebaut
>
> If you need more explanations, I think I have something writen  
> somewhere on
> that particular expression.
>
>
> Yves.
>
>
> --
>
>   Yves Renard (address@hidden)       tel : (33)  
> 04.72.43.87.08
>   Pole de Mathematiques, INSA de Lyon          fax : (33)  
> 04.72.43.85.29
>   20, rue Albert Einstein
>   69621 Villeurbanne Cedex, FRANCE
>   http://math.univ-lyon1.fr/~renard
>
> ---------