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A Perturbation Result for Dynamical Contact Problems

Zitieren Sie bitte immer diese URN: urn:nbn:de:0297-zib-10793
  • This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.

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Metadaten
Verfasserangaben:Corinna Klapproth, Peter Deuflhard, Anton Schiela
Dokumentart:ZIB-Report
Freies Schlagwort / Tag:(visco-)elasticity; Dynamical contact problems; Newmark method; Signorini condition; stability
MSC-Klassifikation:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Hxx Dynamical problems / 74H55 Stability
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Mxx Special kinds of problems / 74M15 Contact
Datum der Erstveröffentlichung:10.07.2008
Schriftenreihe (Bandnummer):ZIB-Report (08-27)
ISSN:1438-0064
ZIB-Reportnummer:08-27
Verlagspublikation:Appeared in: Numer. Math. Theor. Meth. Appl. 2 (2009)
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