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Re: [Getfem-users] non linear elasticity
From: |
Yves Renard |
Subject: |
Re: [Getfem-users] non linear elasticity |
Date: |
Tue, 29 Apr 2008 16:56:29 +0200 |
User-agent: |
KMail/1.9.5 |
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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