[Getfem-users] Theory behind mdbrick_Coulomb_friction.set_augmented_matrix

[Konstantinos Poulios]

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%20ParaView%203.4.0_simple_gears2.png

but I have difficulties to add augmentation to the Lagrange
multipliers for the contact constraints. I 've already read the
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