On the frictionless unilateral contact of two viscoelastic bodies
We consider a mathematical model which describes the quasistatic contact between two deformable bodies. The bodies are assumed to have a viscoelastic behavior that we model with Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the classical Signorini condition with zer...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03212043 |
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| _version_ | 1832563351597613056 |
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| author | M. Barboteu T.-V. Hoarau-Mantel M. Sofonea |
| author_facet | M. Barboteu T.-V. Hoarau-Mantel M. Sofonea |
| author_sort | M. Barboteu |
| collection | DOAJ |
| description | We consider a mathematical model which describes the quasistatic
contact between two deformable bodies. The bodies are assumed to
have a viscoelastic behavior that we model with Kelvin-Voigt
constitutive law. The contact is frictionless and is modeled with
the classical Signorini condition with zero-gap
function. We derive a variational formulation of the problem and
prove the existence of a unique weak solution to the model by
using arguments of evolution equations with maximal monotone
operators. We also prove that the solution converges to the
solution of the corresponding elastic problem, as the viscosity
tensors converge to zero. We then consider a fully discrete
approximation of the problem, based on the augmented Lagrangian
approach, and present numerical results of two-dimensional test
problems. |
| format | Article |
| id | doaj-art-37bc5356d84b45e49294d610f1e10e97 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-37bc5356d84b45e49294d610f1e10e972025-02-03T01:20:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422003-01-0120031157560310.1155/S1110757X03212043On the frictionless unilateral contact of two viscoelastic bodiesM. Barboteu0T.-V. Hoarau-Mantel1M. Sofonea2Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 avenue de Villeneuve, Perpignan 66860, FranceLaboratoire de Théorie des Systèmes, Université de Perpignan, 52 avenue de Villeneuve, Perpignan 66860, FranceLaboratoire de Théorie des Systèmes, Université de Perpignan, 52 avenue de Villeneuve, Perpignan 66860, FranceWe consider a mathematical model which describes the quasistatic contact between two deformable bodies. The bodies are assumed to have a viscoelastic behavior that we model with Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the classical Signorini condition with zero-gap function. We derive a variational formulation of the problem and prove the existence of a unique weak solution to the model by using arguments of evolution equations with maximal monotone operators. We also prove that the solution converges to the solution of the corresponding elastic problem, as the viscosity tensors converge to zero. We then consider a fully discrete approximation of the problem, based on the augmented Lagrangian approach, and present numerical results of two-dimensional test problems.http://dx.doi.org/10.1155/S1110757X03212043 |
| spellingShingle | M. Barboteu T.-V. Hoarau-Mantel M. Sofonea On the frictionless unilateral contact of two viscoelastic bodies Journal of Applied Mathematics |
| title | On the frictionless unilateral contact of two viscoelastic bodies |
| title_full | On the frictionless unilateral contact of two viscoelastic bodies |
| title_fullStr | On the frictionless unilateral contact of two viscoelastic bodies |
| title_full_unstemmed | On the frictionless unilateral contact of two viscoelastic bodies |
| title_short | On the frictionless unilateral contact of two viscoelastic bodies |
| title_sort | on the frictionless unilateral contact of two viscoelastic bodies |
| url | http://dx.doi.org/10.1155/S1110757X03212043 |
| work_keys_str_mv | AT mbarboteu onthefrictionlessunilateralcontactoftwoviscoelasticbodies AT tvhoaraumantel onthefrictionlessunilateralcontactoftwoviscoelasticbodies AT msofonea onthefrictionlessunilateralcontactoftwoviscoelasticbodies |