Variational Formulation of Rate- and State-Dependent Friction Problems

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Elias Pipping - , Freie Universität (FU) Berlin (Autor:in)
  • Oliver Sander - , Rheinisch-Westfälische Technische Hochschule Aachen (Autor:in)
  • Ralf Kornhuber - , Freie Universität (FU) Berlin (Autor:in)

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.

Details

OriginalspracheEnglisch
Seiten (von - bis)377-395
Seitenumfang19
FachzeitschriftZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Jahrgang95
Ausgabenummer4
PublikationsstatusVeröffentlicht - 2015
Peer-Review-StatusJa
Extern publiziertJa

Externe IDs

Scopus 84926316173
ORCID /0000-0003-1093-6374/work/142250569

Schlagworte

Schlagwörter

  • friction, rate-and-state, variational formulation, existence