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Re: [Getfem-users] non linear elasticity

From: jean-yves heddebaut
Subject: Re: [Getfem-users] non linear elasticity
Date: Tue, 29 Apr 2008 18:22:21 +0200


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


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

2.E is the Green-Lagrange strain tensor, also based on the preceding
iteration displacements

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. 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 Renard (address@hidden) tel : (33) Pole de Mathematiques, INSA de Lyon fax : (33)
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE


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