Preprint No.
A-13-03
Elias Pipping, Oliver Sander, Ralf Kornhuber
Variational formulation of rate- and state-dependent friction
problems
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
Mathematics Subject Classification (MSC2010):
65N30, 65N55, 75S05
Language: ENG
Available: Pr-A-13-03.pdf
Contact: Ralf Kornhuber, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, D-14195 Berlin, Germany (kornhuber@math.fu-berlin.de)
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