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Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction

Beispiele der Nichteindeutigkeit und Nichtexistenz der Lösung quasistatischer Kontaktprobleme mit Reibung

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Summary

This work considers a contact problem with friction involving one contact point and two degrees-of-freedom. The contacting structure is linear elastic. Two different models of contact interaction are considered, the classical Signorini unilateral contact law and a normal compliance law. Coulomb's law of friction is used. All possible so-called rate problems are solved, from which one concludes that the quasistatic problem may possess non-uniqueness and non-existence of solutions. In the case of the normal compliance law this can be explained by a softening structural response. For Signorini's law softening explains only some of the possible situations where non-uniqueness can occur.

Übersicht

In dieser Arbeit wird ein Kontaktproblem mit Reibung behandelt, das einen Kontaktpunkt und zwei Freiheitsgrade einschließt. Die kontaktgebende Struktur ist linearelastisch. Zwei verschiedene Modelle der Kontaktwirkung sind berücksichtigt: Erstens das klassische einseitige Signorini-Kontaktgesetz und zweitens ein Gesetz für die Nachgiebigkeit in Normalenrichtung. Das Coulombsche Reibungsgesetz wird verwendet. Alle möglichen sogenannten Geschwindigkeitsprobleme werden gelöst, woraus geschlossen wird, daß das quasistatische Problem Nichteindeutigkeit und Nichtexistenz der Lösung besitzen kann. Im Fall des Nachgiebigkeitsgesetzes kann dieses als abfallende Struktursteifigkeit erklärt werden. Im Fall eines Signorini-Gesetzes erklärt dieses nur einige der möglichen Situationen, wo Nichteindeutigkeit auftreten kann.

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  1. Div. of Solid Mechanics and Strength of Materials Dept. of Mechanical Engineering, Linköping Institute of Technology, S-581 83, Linköping, Sweden

    A. Klarbring

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Klarbring, A. Examples of non-uniqueness and non-existence of solutions to quasistatic contact problems with friction. Ing. arch 60, 529–541 (1990). https://doi.org/10.1007/BF00541909

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