Re: [Getfem-users] Antwort: Re: 2D nonlinear plane stress

[Yves Renard]

Dear Jena,

For an hyperelastic law, the weak form of the static elastic problem can be 
written in the weak form language


"Def F := Id(meshdim)+Grad_u; (F * S) : Grad_test_u"

for u the displacement, F the deformation gradient and S has to contains the 
expression of the second Piola-Kirchhoff stress tensor (you can of course 
express it in term of PK1 also). For instance for a St Venant Kirchhoff law, 
you can write

"Def F := Id(meshdim)+Grad_u; Def E := 0.5*(F'*F-Id(meshdim));  (F * 
(lambda*Trace(E)+2*mu*E)) : Grad_test_u"

where E will be the Green Lagrange deformation tensor and lambda, mu the Lamé 
coefficients.

This gives you some examples of construction of hyperelastic laws. The weak 
form language gives you access to some standard operators (Trace, Det ...) see 
http://getfem.org/userdoc/model_nonlinear_elasticity.html#high-level-generic-assembly-versions


So, if you have the expression of your law in plane stress, it should not be 
very difficult to implement it. But of course you need the expression of the 
law in plane stress. On the construction itself of plane stress hyperelastic 
law, now, I don't know a good reference, unfortunately. 

Best regards,

Yves


----- Original Message -----
From: "Moritz Jena" <address@hidden>
To: "yves renard" <address@hidden>
Cc: "getfem-users" <address@hidden>
Sent: Wednesday, January 16, 2019 2:17:01 PM
Subject: Antwort: Re: [Getfem-users] 2D nonlinear plane stress

Hello Yves,

thank you for your answer. 

I'm afraid I'm not into the topic weak form language and I'm not sure 
where to start with this problem. 

I looked at the chapter in the documentation, however I don't know how to 
describe a plane stress material model with it.

I also studied the examples, that come with the MATLAB-Interface. There 
are a few examples, how to declare a material model with this weak form 
expressions. But I still don't know, how to build this expressions.

Can you give me a approach for this problem or where I can find 
expressions for such a problem?  Is there any literature that you can 
recommend?

Best regards,

Moritz 





Von:    Yves Renard <address@hidden>
An:     Moritz Jena <address@hidden>
Kopie:  getfem-users <address@hidden>
Datum:  09.01.2019 17:17
Betreff:        Re: [Getfem-users] 2D nonlinear plane stress




Dear Moritz Jena,

No, unfortunately, plane stress versions of Hyperelastic laws has not been 
implemented yet.

I would not be so difficult, but as to be made. If you need one in 
particular and have the expression, it is no so difficult to describe it 
with the weak form language.

Best regards,

Yves



----- Original Message -----
From: "Moritz Jena" <address@hidden>
To: "getfem-users" <address@hidden>
Sent: Tuesday, January 8, 2019 4:11:48 PM
Subject: [Getfem-users] 2D nonlinear plane stress

Dear GetFEM-Users,

I use the MATLAB-Interface of GetFEM to create a program that 
automatically solves different models of the same problem.

The problem is three-dimensional, but can be reduced by plain stress 
approximation. (to reduce computing time).

I want to define a nonlinear material with the brick

                gf_model_set(model M, 'add nonlinear elasticity brick', 
[...])

For this nonlinear command it is specified in the description, that in 2D 
always plain strain is used.

So my question is: Is there a way to define a nonlinear material with the 
plain stress approximation? Or is it planned to install such an option in 
a future release?

I hope you can help me with my problem.

Best regards,

Moritz Jena