On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method

0563211 - ÚTIA 2023 RIV CH eng C - Conference Paper (international conference)
Gfrerer, H. - Outrata, Jiří - Valdman, Jan
On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method.
Large-Scale Scientific Computing. Cham: Springer, 2022 - (Lirkov, I.; Margenov, S.), s. 515-523. Lecture Notes in Computer Science, 13127. ISBN 978-3-030-97548-7. ISSN 0302-9743.
[International Conference on Large-Scale Scientific Computing /13./. Sozopol (BG), 07.06.2021-11.06.2021]
R&D Projects: GA ČR(CZ) GF19-29646L
Institutional support: RVO:67985556
Keywords : Contact problems * Tresca friction * Semismooth* Newton method * Finite elements * Matlab implementation
OECD category: Pure mathematics
http://library.utia.cas.cz/separaty/2022/MTR/valdman-0563211.pdf

An equilibrium of a linear elastic body subject to loading and satisfying the friction and contact conditions can be described by a variational inequality of the second kind and the respective discrete model attains the form of a generalized equation. To its numerical solution we apply the semismooth* Newton method by Gfrerer and Outrata (2019) in which, in contrast to most available Newton-type methods for inclusions, one approximates not only the single-valued but also the multi-valued part. This is performed on the basis of limiting (Morduchovich) coderivative. In our case of the Tresca friction, the multi-valued part amounts to the subdifferential of a convex function generated by the friction and contact conditions. The full 3D discrete problem is then reduced to the contact boundary. Implementation details of the semismooth* Newton method are provided and numerical tests demonstrate its superlinear convergence and mesh independence.
Permanent Link: https://hdl.handle.net/11104/0335249