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## Re: [Getfem-users] material law with non-symmetric stiffness

 From: Andriy Andreykiv Subject: Re: [Getfem-users] material law with non-symmetric stiffness Date: Mon, 2 May 2011 15:11:41 +0200

Dear Yves,

Indeed, in my case I am not in a hyperelastic framework. I'm
developing something like a damage model.
But even if I were, I still can formulate an orthotropic linear
elastic material which results in a global non-symmetric stiffness, a
material with conventional energy expression

= \sum_{ijkl} 1/2 C_{ijkl}  E_{ij} E_{kl}

Due to the symmetry of strain tensor E we have ij symmetry and kl
symmetry, but, for an orthotropic (unlike isotropic one) material
C_{ijkl} is not equal C_{klij}  and that causes a non-symmetric global
stiffness.

But now that you pointed me to the fact that symmetry is implied in
asm_nonlinear_elasticity_tangent_matrix with "sym" in assembly
I probably should simply remove the "sym" operator there.

non-linear brick and assemblies, that specify whether the problem is
symmetric (with default true to provide code legacy).

Thank you,
Andriy

>
>
> Dear Andriy,
>
> Since grad_sigma should be the hessian of an elastic energy, it as to be
> symmetric, at least in the hyperelastic framework. I am not a specialist of
> orthotropic material, what is the difference is that case ? You mean that you
> are not in an hyperelastic framework ?
>
> The symmetry is assumed in assembly routines
> (asm_nonlinear_elasticity_tangent_matrix use "M(#1,#1)+=sym(...)") for the
> stiffness matrix.
>
>
> Yves.
>
>
> On lundi 2 mai 2011, Andriy Andreykiv wrote:
>> Dear Getfem users,
>>
>> I would like to use a non-linear elasticity brick with my own material
>> law that has non-symmetric stiffness matrix.
>> It's non-symmetric if you write it with Voigt notations, but of
>> course, two other "standard" symmetries of a full C_{ijkl} tensor are
>> present (i-j symmetry and k-l symmetry).
>> When I looked into getfem_nonlinear_elasticity.h I  found a comment
>> (next to virtual void grad_sigma declaration):
>>
>> "// the result of grad_sigma has to be completely symmetric."
>>
>> Does this comment imply the above mentioned two symmetries or it means
>> that a non-symmetry that also reveals itself
>> in material matrix, written in  Voigt notations, is also not allowed?
>> A simple example would be: Can I use a fully orthotropic material in
>> non-linear elasticity brick?
>> I browsed through the code of "getfem::nonlinear_elem_term " but it
>> doesn't look like any symmetry is required.
>> However, I would like to be sure.
>>
>>                                      Andriy
>>
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>> Getfem-users mailing list
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>
>
> --
>
>  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
>  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
>  20, rue Albert Einstein
>  69621 Villeurbanne Cedex, FRANCE
>  http://math.univ-lyon1.fr/~renard
>
> ---------
>