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.
