Open Access
25 March 2002 A frictionless contact problem for viscoelastic materials
Mikäel Barboteu, Weimin Han, Mircea Sofonea
J. Appl. Math. 2(1): 1-21 (25 March 2002). DOI: 10.1155/S1110757X02000219


We consider a mathematical model which describes the contact between a deformable body and an obstacle, the so-called foundation. The body is assumed to have a viscoelastic behavior that we model with the Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the well-known Signorini condition in a form with a zero gap function. We present two alternative yet equivalent weak formulations of the problem and establish existence and uniqueness results for both formulations. The proofs are based on a general result on evolution equations with maximal monotone operators. We then study a semi-discrete numerical scheme for the problem, in terms of displacements. The numerical scheme has a unique solution. We show the convergence of the scheme under the basic solution regularity. Under appropriate regularity assumptions on the solution, we also provide optimal order error estimates.


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Mikäel Barboteu. Weimin Han. Mircea Sofonea. "A frictionless contact problem for viscoelastic materials." J. Appl. Math. 2 (1) 1 - 21, 25 March 2002.


Published: 25 March 2002
First available in Project Euclid: 30 March 2003

zbMATH: 1035.74040
MathSciNet: MR1897455
Digital Object Identifier: 10.1155/S1110757X02000219

Primary: 74M15 , 74S05
Secondary: 65M60

Rights: Copyright © 2002 Hindawi

Vol.2 • No. 1 • 25 March 2002
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