Re: [Getfem-users] non linear elasticity

[Yves Renard]

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

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