Repository: Freie Universität Berlin, Math Department

Variational formulation of rate- and state-dependent friction problems

Pipping, E. and Sander, O. and Kornhuber, R. (2015) Variational formulation of rate- and state-dependent friction problems. Zeitschrift für angewandte Mathematik und Mechanik (ZAMM), 95 (4). pp. 377-395. ISSN 0044-2267


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We propose a variational formulation of rate- and state-dependent models for the dynamic sliding of a linearly elastic block on a rigid surface in terms of two coupled variational inequalities. Classical Dieterich–Ruina models are covered as special cases. We show existence and uniqueness of solutions for the two spatial subproblems arising from time discretisation. Existence of solutions to the coupled spatial problems is established for Dieterich's state equation through a fixed point argument. We conclude with some numerical experiments that suggest mesh independent convergence of the underlying fixed point iteration, and illustrate quasiperiodic occurrence of stick/slip events.

Item Type:Article
Uncontrolled Keywords:Continuum mechanics, frictional contact problems, gradient flows, finite elements
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1783
Deposited By: Ekaterina Engel
Deposited On:17 Feb 2016 08:33
Last Modified:03 Mar 2017 14:41

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