getfem-users
[Top][All Lists]

## 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

```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)

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

```
```
```
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

---------
```
```

```