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## Re: [Getfem-users] Theory behind mdbrick_Coulomb_friction.set_augmented_

 From: Yves Renard Subject: Re: [Getfem-users] Theory behind mdbrick_Coulomb_friction.set_augmented_matrix Date: Wed, 18 Nov 2009 14:47:49 +0100 User-agent: KMail/1.9.9

```Dear Kostas,

The mdbrick_Coulomb_friction brick contains a certain number of version due to
the fact that it has been adapted to different situations (unstationnary
problems, Barbosa-Hughes augmentation ...).
In fact, I intend to rewrite this brick soon for the new brick system.

There is two type of augmentation. There is the augmentation due to the
augmented lagrangian technique used to solve numerically the problem with a
Newton-Raphson algorithm (this is indeed presented in
http://www.lms.polytechnique.fr/users/khenous/files/coulomb_num.pdf for
instance).

The second augmentation is the Barbosa-Hughes one presented indeed in
http://math.univ-lyon1.fr/~renard/papers/2007_HR_contact.pdf
This is not a mandatory augmentation. The advantage is that it adds a
contribution on the multipliers which helps to solve the system and allow  to
have an inf-sup condition between the space of multipliers and the space of
displacements (for instance, it allows affine displacements and piecewise
constant multipliers). This augmentation is not fully taken into acocunt by
the brick (in fact there is just the possibility to take into account the
additional term wich modifies a bit the contac/friction condition). This
means that the additional term should be added by hand (as it is actually
done in contrib/static_friction.cc )
My question : do you really need this augmentation in your problem ?
If yes, I can give you some additional explanations.

Besides, you propose an algorithm to produce matrices BN and BT. This would be
a very interesting contribution of course !
My idea for the new contact/friction brick should be to write a basic brick
being essentially the same than the old one (BN, BT, gap, r are not computed
by the brick) and some derived bricks (for instance thanks to a virtual
function) which would be able to compute the matrices BN and BT in different
standard situations (elastic/rigid, elastic/elastic conforming mesh,
elastic/elastic non-conforming mesh) given the contact boundaries and the
space of multiplier (and an optional additional stailization / dynamic part).

In the new brick system, there is already a mecanism to basically ensure that
the discrete inf-sup condition is satisfied (it suppresses the multiplier
exceeding dofs). But of course this do no prevent from locking phenomena. So
I don't know if we have to use it for this contact/brick (the problem is when
there is a contact boundary next to a Dirichlet one).

If you are interested in, we could iterate to build this new brick. This
should be interesting and very usefull !

I also intend to write a more general contact/friction brick for large
deplacement/deformation problems. For the moment, this is very prospective
because I would like to build a robust algorithme. I found the existing
algorithm not really satisfactory. So this is for a longer term.

Yves.

On samedi 14 novembre 2009, Konstantinos Poulios wrote:
> I am writing an application for gear calculations based on getfem and
> using the "mdbrick_Coulomb_friction" brick. The first results seem
> encouraging:
>
> http://files.ubuntu-gr.org/forum/logari81/getfem/Screenshot-Kitware%20ParaV
>iew%203.4.0_simple_gears2.png
>
> but I have difficulties to add augmentation to the Lagrange
> relevant material from http://math.univ-lyon1.fr/~renard/ -->
> Publications and
> http://www.lms.polytechnique.fr/users/khenous/publications.htm but I
> am not yet in a position to derive the part of the tangent matrix
> corresponding to the "set_augmented_matrix" method myself. Up to now
> all my attempts to derive this matrix yield to a zero matrix. I have
> already studied the contrib/static_friction.cc example but it didn't
> help me to resolve my question.
>
> I would like to ask for some hints or bibliography on the derivation
> of the tangent matrix of the "mdbrick_Coulomb_friction" brick in the
> case of augmentation. Please take into account that I haven't studied
> Mathematics but Mechanical Engineering and most of the books I have
> read on contact mechanics are from the point of view of an Engineer.
> Actually I understand more or less the theory presented in e.g.
> http://math.univ-lyon1.fr/~renard/papers/2007_HR_contact.pdf and
> http://www.lms.polytechnique.fr/users/khenous/files/coulomb_num.pdf .
> I also understand the implementation in getfem_Coulomb_friction.h
> pretty well. What I miss are some steps between the abstract theory
> and its practical implementation.
>
> Additionally I would like to offer my help to expand the contact
> mechanics infrastructure in getfem. I have already programmed a quite
> general contact searching algorithm which derives the "BN" and "gap"
> arrays for the "mdbrick_Coulomb_friction" brick. I could also help
> with the documentation of the contact brick.
>
> Best Regards
>
> Kostas
>
> _______________________________________________
> Getfem-users mailing list
> https://mail.gna.org/listinfo/getfem-users

--

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

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