A Perturbation Result for Dynamical Contact Problems
Please always quote using this 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.
Author: | Corinna Klapproth, Peter Deuflhard, Anton Schiela |
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Document Type: | ZIB-Report |
Tag: | (visco-)elasticity; Dynamical contact problems; Newmark method; Signorini condition; stability |
MSC-Classification: | 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 | |
Date of first Publication: | 2008/07/10 |
Series (Serial Number): | ZIB-Report (08-27) |
ISSN: | 1438-0064 |
ZIB-Reportnumber: | 08-27 |
Published in: | Appeared in: Numer. Math. Theor. Meth. Appl. 2 (2009) |