Orateur
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.
