Journal article
A frictionless contact problem for viscoelastic materials
Journal of Applied Mathematics, Vol.2(1), pp.1-21
2002
DOI: 10.1155/S1110757X02000219
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.
Details
- Title: Subtitle
- A frictionless contact problem for viscoelastic materials
- Creators
- Mikäel BarboteuMircea SofoneaWeimin Han
- Resource Type
- Journal article
- Publication Details
- Journal of Applied Mathematics, Vol.2(1), pp.1-21
- DOI
- 10.1155/S1110757X02000219
- ISSN
- 1110-757X
- eISSN
- 1687-0042
- Grant note
- DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-9874015
- Language
- English
- Date published
- 2002
- Academic Unit
- Mathematics
- Record Identifier
- 9983985804402771
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