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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
Abstract:
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
DOI: 10.1002/zamm.201300062
Publication:Zeitschrift für angewandte Mathematik und Mechanik: ZAMM
Journal of applied mathematics and mechanics (2013)