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## Re: [Getfem-users] mesh_deformation

 From: Andriy Andreykiv Subject: Re: [Getfem-users] mesh_deformation Date: Thu, 27 Dec 2018 11:48:17 +0100

Dear Zhenghuai Guo,

Sorry for the late response. You're doing everything correct except your elements are not isoparametric, as temporary_mesh_deformator requires (this is it's current limitation, of course).
Geometric transformation of your elements is linear (you generated linear triangles with three vertices in GMSH), while the element type is FEM_PK(2, 2), meaning
that they have 6 degrees of freedom per element. You either need to create quadratic mesh in GMSH (it has a button "Order" or something), or, alternatively, you'd need to use FEM_PK(2, 1) linear interpolation

Regarding the software I use for meshing. I used to use GMSH a lot as well. It does a good job once you learn it's ways. It's quite ok for reasonably small meshes. Now we use Getfem in our company and have our internal in-house mesher.

Best regards,
Andriy

On Mon, 17 Dec 2018 at 02:28, Zhenghuai Guo <address@hidden> wrote:

Hi Andriy,

Could you please again help me for the following?

1. I generate an mesh from gmsh (‘Mesh_3.msh’ as attached). Then I run the code ‘myexperiment.cc’ as attached. It is basically for isotropic linear eleasticity.

Everything is fine if I delete the line 101 ‘auto deformator = getfem::temporary_mesh_deformator<getfem::model_real_plain_vector>(mf_u, U, true, false);’

I can get a displacement field as in the figure below

If I activate this line 101, then I get

Level 3 Warning in getfem_import.cc, line 233:   All regions must have different number!

Mesh exported: 'mesh.vtk'

defined boundary: 'bound for whole boundary' 'Dirichlet_boundary for Dirichlet boundary' 'Neumann_boundary for Neumann boundary'

set fem mf_u: 'FEM_PK(2, 2)'

set mim mim: 'IM_TRIANGLE(2)'

model bullt: 'model'

add scalar_data lambda, mu: 'lambda' 'mu'

add fixed_size_data Dirichlet_value, Fdata: 'Dirichlet_value' 'Fdata'

Trace 2 in getfem_models.cc, line 4325: Mass term assembly for Dirichlet condition

Trace 2 in getfem_models.cc, line 4362: Source term assembly for Dirichlet condition

Trace 2 in getfem_models.cc, line 3446: Generic linear assembly brick: generic matrix assembly

Trace 2 in getfem_models.cc, line 4325: Mass term assembly for Dirichlet condition

Trace 2 in getfem_models.cc, line 4362: Source term assembly for Dirichlet condition

Trace 2 in getfem_models.cc, line 3293: Generic source term assembly

Trace 2 in getfem_models.cc, line 3300: Source term: generic source term assembly

Trace 2 in getfem_models.cc, line 3307: Source term: generic matrix assembly

condition number: 14972.4

model solved

terminate called after throwing an instance of 'gmm::gmm_error'

what():  Error in ../src/getfem/getfem_deformable_mesh.h, line 112 void getfem::temporary_mesh_deformator<VECTOR>::deforming_mesh_(VECTOR&) [with VECTOR = std::vector<double>]:

dimension of dof is greater than 3

and the displacement field is as in the below figure

I try to find out what the error means and solve, and I still can’t. The line 101 ‘auto deformator = getfem::temporary_mesh_deformator<getfem::model_real_plain_vector>(mf_u, U, true, false);’ is after line where I export the displacement field U, but the line 101 affect the export of U, which I don’t understand.

1. Could you please let me know what software or approach you normally use for mesh generation for import to Getfem?

Thank you very much

Regards

Zhenghuai Guo

From: Zhenghuai Guo
Sent: Tuesday, December 11, 2018 12:15 AM
Subject: RE: [Getfem-users] mesh_deformation

Oh Thank you Andriy, I think I got confused by myself. The reason is that I already used getfem::vtk_export exp("mesh.vtk", false); above.

Then I do getfem::vtk_export exp("results/displacement_" + std::to_string(n) + ".vtk", false);  It gave error of exp was previously declared.

Now it works. Thank you .

Regards

Zhenghuai Guo

Sent: Tuesday, December 11, 2018 12:02 AM
Subject: Re: [Getfem-users] mesh_deformation

" But in C++, I can’t repeatedly use getfem::vtk_export exp(filename, false) in each time step with a new filename value.  "

Why? Yes you can. For instance, if you have a step number

int step;

and you increment it then you simply post-process inside the loop:

for (step = 0; step < NStep; ++step)

{

//calculation

getfem::vtk_export exp("result_" + std::to_string(step) + ".vtk", false);

}

Best regards,

Andriy

On Mon, 10 Dec 2018 at 13:57, Zhenghuai Guo <address@hidden> wrote:

Thank you Roman,

I will need to digest what you suggested and will let you know how it goes.

In the meantime, can you please advise: how to export a time series mf in .VTK format in C++.

In Python, it is quite easy using ‘model.export_to_vtk('results/displacement_%d.vtk' % n, U) ‘in each time step. The file names can be set to be displacement _1.vtk , displacement _2.vtk, displacement _3.vtk and so on.

But in C++, I can’t repeatedly use getfem::vtk_export exp(filename, false) in each time step with a new filename value.

Thank you very much

Regards

Zhenghuai Guo

Sent: Sunday, December 9, 2018 8:17 PM
Subject: Re: [Getfem-users] mesh_deformation

Dear Zhenghuai Guo,

Probably this is not exactly what you requested, but I think can be helpful. Instead of dealing
with mesh connectivity you could use features of mesh_fem. To get the positions of points
on face you can do:

mesh_fem -> dofs_on_face -> poins related to dofs.

In mesh_fem there is a method:
ind_dof_face_ct getfem::mesh_fem::ind_basic_dof_of_face_of_elements(size_type_cv, short f);

It gives an array of dof numbers lying on a convex face.
Then you can use the method:
base_node::mesh_fem::point_of_basic_dof (size_type d);

The only thing to be careful is to properly select mesh_fem type, for instance Lagrangian one with
linear shape functions.

This way of getting points on face may seem strange but it is a direct use of GetFEM API
and you will not have do dig deeper into GetFEM internals.

Regards,

Roman

December 9, 2018 9:43 AM, "Zhenghuai Guo" <address@hidden> wrote:

Hi Andriy,

Your advice help me a lot. I now try to make some simple c++ script in getfem. The compile and
build works fine.

I have one more question: how to get the points in a particular face, if we know the convex and
fact index?

I can see that we can do ‘mesh.convex(i).points()’ or ‘mesh.points()[i]’. But we can’t do
‘mesh.faces(i).points()’.

The reason I ask for this is that I would like to have the capacity to define region based spatial
coordinates.

Thank you very much

Zhenghuai Guo

Sent: Monday, December 3, 2018 5:12 AM
Subject: Re: [Getfem-users] mesh_deformation

Dear Zhenghuai Guo,

The installation and building of getfem and the tests are explained in the manual.

After getfem is installed, you can build all the examples with the command:

make tests

If you want to build a specific example, say laplacian_with_bricks, just type

make laplacian_with_bricks

The make script will call the compiler to build the object file and subsequently link it against
the library.

Your attempt to build elastostatic example is close, but not sufficient: you're compiling your
code, but not

linking against getfem. When you type "make laplacian_with_bricks", you will see the output of the
exact

commands necessary to compile and link against the library. You can use these exact commands to
build

your source file into an getfem based program.

Best regards,

Andriy

On Sat, 1 Dec 2018 at 21:16, Zhenghuai Guo <address@hidden> wrote:

Dear Andriy,

I try your suggestions - using im_data for the coefficients - in python which are working fine.
Thank you very much.

But I still have problem in deforming the mesh in Python – simply don’t know how to call the
‘temporary_mesh_deformator’ in Python. I guess I should do it in C++.

I don’t really use C++ too much. Could you please let me know where the demos are for the C++?

I can see that in the folder ‘getfem-5.3/tests’, there are some ‘.cc’ test files – are they the
demos? I try to compile it : ‘g++ elastostatic.cc -o elastostatic’, but it did not go through (give
the message as attached). I am not sure if I did it right or simply because I did not install the
getfem right in the first place.

Thank you very much

Kind regards

Zhenghuai Guo

Sent: Wednesday, November 21, 2018 9:53 PM
Subject: Re: [Getfem-users] mesh_deformation

Dear Zhenghuai Guo,

For 1 you don't need to do anything. All the variables in the next step remain from the last step.
In some cases, if your variable has two versions (old and current, for instance) you need to call
model::next_iter() to copy all the old versions of variable to the current.

But if the variable doesn't have the two versions you don't need that. Normally we want to have two
versions of variables when our formulations use their increments.

For 2 you don't really need to add the linear elastic term with your own code, as the actual
function add_isotropic_linearized_elasticity_brick uses high-level assembly internally. Here is
it's source code

from getfem_models.cc

size_type add_isotropic_linearized_elasticity_brick(model &md, const mesh_im &mim, const
std::string &varname, const std::string &dataexpr1, const std::string &dataexpr2, size_type region,
const std::string &dataname3) { std::string test_varname = "Test_" +
sup_previous_and_dot_to_varname(varname); std::string expr1 =
"((("+dataexpr1+")*(Div_"+varname+"-Div_"+dataname3
+test_varname; std::string expr2 = "(Div_"+varname+"*(("+dataexpr1+")*Id(meshdim))"
true); workspace.add_expression(expr2, mim, region); model::varnamelist vl, vl_test1, vl_test2, dl;
bool is_lin = workspace.used_variables(vl, vl_test1, vl_test2, dl, 2); if (is_lin) { pbrick pbr =
std::make_shared<iso_lin_elasticity_new_brick> (expr2, dataname3); model::termlist tl;
tl.push_back(model::term_description(varname, sup_previous_and_dot_to_varname(varname), true)); if
(dataname3.size()) dl.push_back(dataname3); return md.add_brick(pbr, vl, dl, tl, model::mimlist(1,
&mim), region); } else { return add_nonlinear_generic_assembly_brick (md, mim, dataname3.size() ?
expr1 : expr2, region, false, false, "Linearized isotropic elasticity (with nonlinear
dependance)"); }}
It's c++, but python logic would be similar.

Regarding the source code you've attached, I see that you still add the elastic constants as a
fixed size data. As I mentioned in the last email, you need to have different constants for every
integration point

of your model. Hence they have to be im_data.

Best regards,

Andriy

On Sun, 18 Nov 2018 at 20:47, Zhenghuai Guo <address@hidden> wrote:

Dear Andriy,

Thank you for the advice. You understand correctly about what I am trying to achieve. The problems
I am having now are to how to (1) use an updated deformed mesh and (2) consider the
displacement/stress value of previous timestep as the initial condition at each new time step.

* If I use Isotropic_linearized_elastic_brick, how can I pass the displacement and stress values
from one time step to another? At each timestep, I would like the initial condition to take into
account the state (e.g. displacement and stress) of last timestep. I am not sure maybe it does it
automatically or not.
* I am trying to use high level assembly string language to carry out linear elasticity. I am
guessing, by doing this I can be more free. And maybe I can consider the displacement/stress value
of previous timestep as the initial condition at each new time step.
Could you please have a look at the attached small code? I try to add the assembly string of

but, when I run the code, it appear with some problem – although it does not give error, but it

Thank you very much

Regards

Zhenghuai Guo

Sent: Friday, November 16, 2018 11:03 PM
Subject: Re: [Getfem-users] mesh_deformation

Dear Zhenghuai Guo,

If I understand correctly, you're trying to model creep with contact. If so, then you can probably
assume that your elastic properties are weakly coupled with stress. In that case you can probably
just update your elastic properties every time step.

So, you need to write a loop where you change the properties every step. Here are some ideas

1) Your elastic properties lambda and mu cannot be fixed sized constants, as they will depend on
stress values throughout the domain. The logical way to handle this is

by setting them as a so-called im_data, which is a field defined on Gauss points (on mesh_im

2) Isotropic linearized elastic brick does not compute and store stress field. You will need to
define stress field as im_data too and compute it from your solution

using probably high-level assembly syntax

&imd_stress, base_vector &stress_result_vector);

3) The whole calculation should look like this:

initialize the elastic properties as im_data

create im_data for the stress

while(t < T)

{

md.solve();

compute the stresses from the displacement field using high-level assembly syntax interpolations
compute the new values for the elastic properties with high-level assembly syntax interpolations
post-process;
t = t + delta T;
}

Best regards,
Andriy

On Fri, 16 Nov 2018 at 04:42, Zhenghuai Guo <address@hidden> wrote:

Dear Andriy,

I am planning to do a time dependent deformation with consideration of the contact and friction. I
would like to apply the elasticity theory with Young’s modulus being a function of time and local
stress value.

* If I use add_isotropic_linearized_elasticity_brick (mim, varname, dataname_lambda, dataname_mu,
region=None), how can I make the Young’s modulus time and stress dependent? In the test examples
e.g. in demo_tripod.py, Young’s modulus is only added by the method add_initialized_data as a
constant scalar value.
* If I carry out elasticity formulation by a approach like the one in demo_tripod_alt.py using low
level approach to building the linear system by hand, can I in the meantime apply together the
region, dispname, wname=None)?
Thank you very much

Best regards

Zhenghuai Guo

Sent: Thursday, November 8, 2018 8:56 PM
Subject: Re: [Getfem-users] mesh_deformation

Dear Zhenghuai Guo,

You can build getfem and getfem based programs using either GCC c++ compiler for Linux based
systems
(read Page 5 of the user doc:
or with Microsoft Visual Studio (you can use free Community edition). You can find MSVC solution in
msvc directory of the distribution.
Unfortunately, the solution for MSVC is not kept up-to-date and you would need to re-add all getfem
sources to it to make it work.

You can deform your mesh with a simple call:
auto deformator = temporary_mesh_deformator(mf, U, true, false);
//the first true means "deform on creation", the second false means "do not restore the mesh back
when temporary_mesh_deformator reaches the end of life"
mf - is the mesh_fem for your displacement field and U is the displacement vector with
gmm::vect_size(U) = mf.nb_dof();

Best regards,
Andriy

On Thu, 8 Nov 2018 at 01:15, Zhenghuai Guo <address@hidden> wrote:

Dear Andriy,

Regarding creep, at the moment I only use liner_elasticity_brick with young’s modulus being changed
on each time-step. This is just to start with. I am new in Getfem in fact.

* Are you using c++ to run getfem? If so, can you give some hints how I can to it? I can’t see any
instruction about setting up for c++.
* If you don’t use c++, how do you normally use the getfem::temporary_mesh_deformator (from
getfem_deformable_mesh.h) or other C functions?
I was trying to see if it is possible to use this function in Python interface by using SWIG or
Python.Boost. But it is far beyond my knowledge.

Thank you very much

Regards

Zhenghuai Guo

Sent: Wednesday, November 7, 2018 8:32 PM
Subject: Re: [Getfem-users] mesh_deformation

Dear Zhenghuai Guo,

I don't use Python interface much, but your assumption is correct, using
getfem::temporary_mesh_deformator (from getfem_deformable_mesh.h) you can apply displacement field
to the mesh.
By default temporary_mesh_deformator will deform the mesh and un-deform it in the destructor,
unless you build it with the argument to_be_restored=false.
I only assume that you can do it with Python too.

I'm not really experienced with creep, but intuitively I would assume that you can also use large
deformation formulation to account for the change in geometry.
Or it's not how you intend it?

primarily for post-processing, not calculation. If you intend to use it solely for
post-processing than you can easily achieve it nowadays with Paraview, were you import a vtk file,
warp the result with a displacement field and take a desired slice.

Best regards,
Andriy
On Sat, 3 Nov 2018 at 12:33, Zhenghuai Guo <address@hidden> wrote:

Could you please advise how I and deform a mesh according to a displacement field?

I am trying to simulate a time dependent deformation of a cylinder like object using
python-interface. After applying stress the object creeps with time.

I think I can just go with many small time steps. In each time step, I would like to update and
deform the mesh according to the displacement calculated as a function of time. And the deformed
mesh will be an input for next time step.

I can see there is some related information such as (1) ‘getfem_deformable_mesh.h’ in page 18 in
‘getfem::slicer_apply_deformation’ in
http://getfem.org/userdoc/export.html#getfem::slicer_apply_deformation . But I can find details
examples.

Thank you very much

Zhenghuai Guo

Tyree Xray CT network facility, School of Minerals and Energy Engineering Resources, UNSW Sydney

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