# Congrès d'Analyse Numérique pour les Jeunes - 2020

Dec 3 – 4, 2020
Virtuel
Europe/Paris timezone

## A symmetric algorithm for solving mechanical contact problems using FreeFEM

Dec 4, 2020, 3:30 PM
30m
Zoom (Virtuel)

### Zoom

#### Virtuel

Salle 1 : https://zoom.us/j/94929969299 Salle 2 : https://zoom.us/j/98740649245 Salle 3 : https://zoom.us/j/99534523679

### Speaker

Mr Houssam Houssein (LJLL - Sorbonne Université)

### Description

The mechanical Contact between two bodies is one of the most difficult problems in solid mechanics, indeed the material non-linearity must be taken into account and the contact area is unknown. In the case of frictional contact another non-linearity must be considered and makes the problem even more difficult. There exist several algorithms to solve the contact problems [3], most of them involve the concept of master/slave, which prevents the penetration of the slave body into the master one, and therefore causes the non-symmetry of the algorithm.

In this work the contact problem is formulated into a constrained minimization one. In the first part, we will present some algorithms, developed using FreeFEM [1], treating Signorini's problem [2] (contact between a body and a rigid foundation). In the second part two algorithms treating the contact between two bodies are presented, the first algorithm uses the penalty method, and the second one uses the interior-point method. One of the advantages of these two algorithms is the symmetric behavior, in addition the Interior point optimizer (IPOPT) [4] is used in order to solve the constrained minimization problem.

Bibliography

[1] Frédéric Hecht, New development in FreeFem++, Journal of numerical mathematics, vol. 20, no 3-4, p. 251-266, 2012.
[2] Antonio Signorini, Sopra alcune questioni di elastostatica, Atti della Societa Italiana per il Pro- gresso delle Scienze, 21(II):143–148, 1933.
[3] Peter Wriggers, Computational Contact Mechanics, Second Edition, Springer-Verlag, 2006.
[4] Andreas Wächter and Lorenz T. Biegler , On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical programming, Springer, vol. 106, no 1, p. 25-57, 2006.

### Primary author

Mr Houssam Houssein (LJLL - Sorbonne Université)

### Co-authors

Dr Simon Garnotel (Airthium SAS) Prof. Frédéric Hecht (LJLL - Sorbonne Université)

### Presentation materials

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