A frictionless contact problem for viscoelastic materials

Mikäel Barboteu, Weimin Han and Mircea Sofonea

Journal of Applied Mathematics, 2002, vol. 2, issue 1, 1-21

Abstract: 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.

Date: 2002
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https://doi.org/10.1155/S1110757X02000219

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2:y:2002:i:1:p:1-21

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