359	RWTH Publication No: 230040        2013        IGPM359.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)