|Preprint-No.:||< 359 >||Published in:||March 2013||PDF-File:||IGPM359_k.pdf|
|Title:||Variational Formulation of Rate- and State-Dependent Friction Problems|
|Authors:||Elias Pipping, Oliver Sander, Ralf Kornhuber|
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.
|Keywords:||Continuum mechanics, frictional contact problems, gradient flows, finite elements|
|Publication:||Zeitschrift für angewandte Mathematik und Mechanik: ZAMM |
Journal of applied mathematics and mechanics (2013)