A frictionless contact problem for viscoelastic materials
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...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X02000219 |
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| _version_ | 1832561294076542976 |
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| author | Mikäel Barboteu Weimin Han Mircea Sofonea |
| author_facet | Mikäel Barboteu Weimin Han Mircea Sofonea |
| author_sort | Mikäel Barboteu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-848d8cb37bf2442a8026daa5047d3243 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-848d8cb37bf2442a8026daa5047d32432025-02-03T01:25:28ZengWileyJournal of Applied Mathematics1110-757X1687-00422002-01-012112110.1155/S1110757X02000219A frictionless contact problem for viscoelastic materialsMikäel Barboteu0Weimin Han1Mircea Sofonea2Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, Perpignan 66860, FranceDepartment of Mathematics, University of Iowa, Iowa, IA 52242, USALaboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, Perpignan 66860, FranceWe 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.http://dx.doi.org/10.1155/S1110757X02000219 |
| spellingShingle | Mikäel Barboteu Weimin Han Mircea Sofonea A frictionless contact problem for viscoelastic materials Journal of Applied Mathematics |
| title | A frictionless contact problem for viscoelastic materials |
| title_full | A frictionless contact problem for viscoelastic materials |
| title_fullStr | A frictionless contact problem for viscoelastic materials |
| title_full_unstemmed | A frictionless contact problem for viscoelastic materials |
| title_short | A frictionless contact problem for viscoelastic materials |
| title_sort | frictionless contact problem for viscoelastic materials |
| url | http://dx.doi.org/10.1155/S1110757X02000219 |
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