Dear Kostas,
once again, thank you for pointing out where the problem is!
As soon as i have some time, it would be a pleasure to have a look and
trying to fix this. Thanks a lot!
Regarding the question in my second message in this thread about the
computation of the divergence of a tensor field, arising from the gradient
of an existing variable in a model, do you have any idea?
BR,
David.
Le sam. 28 mai 2022 à 22:10, Konstantinos Poulios <logar...@googlemail.com>
a écrit :
> I see now that Yves has left a comment "to be verified":
>
> // Second derivative
> void second_derivative(const arg_list &args, size_type, size_type,
> base_tensor &result) const { // To be verified
>
> in the second derivative of matrix_j2_operator in
> getfem_nonlinear_elasticity.cc, so maybe you can help by checking/fixing
> this.
>
> BR
> Kostas
>
>
>
> On Sat, May 28, 2022 at 10:05 PM Konstantinos Poulios <
> logar...@googlemail.com> wrote:
>
>> Dear David,
>>
>> It works for me with
>> model.add_nonlinear_generic_assembly_brick(mim,
>> "paramsIMR(1)* ( Matrix_j1(F*F') - 3 )\
>> + paramsIMR(2)* (
>> Matrix_i2(F*F')*pow(Det(F*F'),-2/3) - 3 )")
>> so you must have hit a bug in Matrix_j2.
>>
>> BR
>> Kostas
>>
>> On Sat, May 28, 2022 at 4:42 PM David Danan <daviddanan9...@gmail.com>
>> wrote:
>>
>>> Dear Yves,
>>>
>>> first, thanks for your detailed answers!
>>>
>>> For the first question, at this point, i guess it's much more convenient
>>> at this point to share a script containing a minimal (not) working test
>>> regarding this difference.
>>> I have kept the incompressibility brick in both cases.
>>>
>>> For the second question, it seems clear, thanks.
>>> For the third question, providing the expression of the stress tensor
>>> directly instead is fine by me, it's not very difficult using the
>>> invariants already available in the GWFL combined with some macro.
>>>
>>> While i am at it, i have another question.
>>> It is somehow related to the one in the following thread but for the
>>> divergence of a tensor field
>>> https://lists.nongnu.org/archive/html/getfem-users/2015-03/msg00009.html
>>>
>>> I would like to check the satisfaction of the equilibrium equation (i.e.
>>> div(P) + f0, where Pi is a stress tensor and f0 is a volumic force). To do
>>> so, i gave it a try without volumic forces
>>> value=gf.asm_generic(mim=mim, order=0, expression=
>>> "Norm_sqr(Div(clambda*Trace(Green_Lagrange_E)*Id(2)+2*cmu*Green_Lagrange_E))",
>>> model=model,region=-1)
>>> where Green_Lagrange_E is a macro defined by
>>> model.add_macro("epsilon", "(Grad_u+(Grad_u)')/2")
>>> model.add_macro("Green_Lagrange_E", "epsilon+ (Grad_u)'*Grad_u/2")
>>> but it failed (Error in macro expansion. Only variable name are allowed
>>> for macro parameter preceded by Grad_ Hess_ Test_ or Test2_ prefixes)
>>>
>>> Next, i tried to check whether i could at least apply the Div operator
>>> to Grad_u directly instead, like that
>>> value=gf.asm_generic(mim=mim, order=0, expression=
>>> "Norm_sqr(Div(Grad_u))", model=model,region=-1)
>>> but it also failed, Grad_u was not recognized.
>>>
>>> Is there a way to do that? I see that it's possible to have access to
>>> the hessian of the model variables; is rebuilding div(P) from the hessian
>>> the only way to compute this quantity?
>>> Best regards,
>>>
>>> David.
>>>
>>>
>>> Le jeu. 26 mai 2022 à 10:17, <yves.ren...@insa-lyon.fr> a écrit :
>>>
>>>> Dear David,
>>>>
>>>> I do not see any reason why your expression for the Mooney-Rivlin hyper
>>>> elastic law would give a different result than the brick. At least if of
>>>> cours you keep the
>>>> incompressible brick
>>>> md.add_finite_strain_incompressibility_brick(mim, 'u', 'p')
>>>> (note that using sqr(expr) instead of pow(expr,2) is slightly more
>>>> efficient).
>>>>
>>>> Concerning the plane strain approximation, it is a priori possible to
>>>> do this in GWFL, yes. You can define a 3D matrix from your 2D gradient and
>>>> use the 3D hyperelastic law.
>>>>
>>>> For the computation of the Von Mises stress from the potential, it is a
>>>> little bit more tricky because the automatic differentiation of Getfem will
>>>> give you the directional derivative (in the direction of the test
>>>> function). So may be it is possible to extract the components with a
>>>> specific choice of test functions, but it could be not so easy ... I never
>>>> done that. Unfortunately it is preferable to give the expression of the law
>>>> in term of stress tensor directly.
>>>>
>>>> Best regards,
>>>>
>>>> Yves
>>>>
>>>> ------------------------------
>>>> *De: *"David Danan" <daviddanan9...@gmail.com>
>>>> *À: *"getfem-users" <getfem-users@nongnu.org>
>>>> *Envoyé: *Lundi 23 Mai 2022 13:41:14
>>>> *Objet: *[Getfem-users] Questions about user-defined strain energy
>>>>
>>>> Dear Getfem-users,
>>>>
>>>> to check whether i understand correctly the implementation (and because
>>>> it's actually much clearer in my code that way), i am trying to replace
>>>> some predefined bricks for strain energy by the equivalent version using
>>>> GWFL.
>>>> For that, i have several questions
>>>>
>>>> *First question*
>>>> For instance
>>>> lawname = 'SaintVenant Kirchhoff'
>>>> clambda,cmu = params["clambda"],params["cmu"]
>>>> model.add_initialized_data('paramsSVK', [clambda, cmu])
>>>> idBrick=model.add_finite_strain_elasticity_brick(mim, lawname, 'u',
>>>> 'paramsSVK')
>>>> becomes
>>>> clambda,cmu = params["clambda"],params["cmu"]
>>>> model.add_initialized_data('paramsSVK', [clambda, cmu])
>>>> idBrick=model.add_nonlinear_generic_assembly_brick(mim,
>>>> "(paramsSVK(1)/2)*pow(Trace(Green_Lagrange_E),2)+paramsSVK(2)*Trace(Green_Lagrange_E'*Green_Lagrange_E)"
>>>> )
>>>>
>>>> And the results seems to be the same.
>>>> However, for the incompressible Mooney Rivlin strain energy case, it
>>>> does not behave as i expected
>>>>
>>>> Using the example there as a basis in a 3D case
>>>>
>>>> https://github.com/getfem-doc/getfem/blob/master/interface/tests/python/demo_nonlinear_elasticity.py
>>>> and after some simplifications
>>>>
>>>> I have tried to replace the last line in
>>>> lawname = 'Incompressible Mooney Rivlin'
>>>> model.add_initialized_data('paramsIMR', [1,1])
>>>> model.add_finite_strain_elasticity_brick(mim, lawname, 'u', 'paramsIMR'
>>>> )
>>>> By this
>>>> model.add_nonlinear_generic_assembly_brick(mim,
>>>> "Incompressible_Mooney_Rivlin_potential(Grad_u,
>>>> [paramsIMR(1);paramsIMR(2)])")
>>>> Which was exactly the same, of course. Next, i have tried to replace it
>>>> by these lines
>>>> model.add_macro("F", "Grad_u+Id(3)")
>>>> model.add_nonlinear_generic_assembly_brick(mim, "paramsIMR(1)* (
>>>> Matrix_j1(Right_Cauchy_Green(F)) - 3 )+ paramsIMR(2)* (
>>>> Matrix_j2(Right_Cauchy_Green(F)) - 3 )")
>>>> Which failed to converge
>>>>
>>>> I thought this expression was consistent with the implementation of
>>>> Mooney_Rivlin_hyperelastic_law::strain_energy and the compute_invariants
>>>> here
>>>>
>>>> http://download-mirror.savannah.gnu.org/releases/getfem/doc/getfem_reference/getfem__nonlinear__elasticity_8cc_source.html
>>>> and the documentation
>>>>
>>>> https://getfem.org/userdoc/model_nonlinear_elasticity.html?highlight=finite%20strain
>>>> But, clearly, i am missing something. Could you explain what I am doing
>>>> wrong?
>>>>
>>>> Second question
>>>> In a 2D case, i would like to be able to use either a plane strain
>>>> approximation based on a given strain energy expression in 3D.
>>>> In the implementation, it is nicely done in scalar_type
>>>> plane_strain_hyperelastic_law::strain_energy there
>>>>
>>>> http://download-mirror.savannah.gnu.org/releases/getfem/doc/getfem_reference/getfem__nonlinear__elasticity_8cc_source.html
>>>>
>>>> Is it possible to do the same using the GWFL?
>>>>
>>>> *Third question*
>>>> I would like to be able to compute the von-mises field for any strain
>>>> energy function.
>>>>
>>>> If It is an existing brick, the method
>>>> md.compute_finite_strain_elasticity_Von_Mises(lawname, 'u', 'params',
>>>> mfdu)
>>>> will do the trick just fine.
>>>>
>>>> If it's not the case, i guess i can use something akin to the actual
>>>> implementation of compute_finite_strain_elasticity_Von_Mises
>>>> <http://download-mirror.savannah.gnu.org/releases/getfem/doc/getfem_reference/namespacegetfem.html#a9166bc2065a4f2b5633e2e933ec3e693>
>>>>
>>>> std::string expr = "sqrt(3/2)*Norm(Deviator(Cauchy_stress_from_PK2("
>>>> + adapted_lawname + "_PK2(Grad_" + varname + "," + params + "),Grad_"
>>>> + varname + ")))";
>>>> ga_interpolation_Lagrange_fem(md, expr, mf_vm, VM, rg);
>>>> }
>>>>
>>>> combined with local_projection to get the value at the elements.
>>>> The question is: is it possible to compute Piola Kirchhoff 2 from the
>>>> strain energy within the GWFL expression given to local_projection?
>>>> I have the impression it's the only thing i need to be able to do what
>>>> i want.
>>>> Let W be a strain energy function and E be the Green-Lagrange tensor
>>>> (defined as macros, let's say), is Diff(W, E) doing exactly what i am
>>>> expecting for this purpose?
>>>> If it's not the case, is there another way to do it?
>>>>
>>>> Thank you in advance,
>>>> kind regards,
>>>> David.
>>>>
>>>>
