Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage
We consider the quasistatic Signorini′s contact problem with damage for elastic-viscoplastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. We provide a variational f...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03202023 |
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| _version_ | 1832563350520725504 |
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| author | J. R. Fernández M. Sofonea |
| author_facet | J. R. Fernández M. Sofonea |
| author_sort | J. R. Fernández |
| collection | DOAJ |
| description | We consider the quasistatic Signorini′s contact problem with damage for elastic-viscoplastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. We provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution of the model. We then introduce and study a fully discrete scheme for the numerical solutions of the problem. An optimal order error
estimate is derived for the approximate solutions under suitable solution regularity. Numerical examples are presented to show the performance of the method. |
| format | Article |
| id | doaj-art-348a3af26c8646d194e445db61c3ab5b |
| 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-348a3af26c8646d194e445db61c3ab5b2025-02-03T01:20:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422003-01-01200328711410.1155/S1110757X03202023Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damageJ. R. Fernández0M. Sofonea1Departamento de Matemática Aplicada, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Universitario Sur, Santiago de Compostela 15782, SpainLaboratoire de Thétorie des Systètmes, Université de Perpignan, 52 aven ue de Villeneuve, Perpignan Cedex 66860, FranceWe consider the quasistatic Signorini′s contact problem with damage for elastic-viscoplastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. We provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution of the model. We then introduce and study a fully discrete scheme for the numerical solutions of the problem. An optimal order error estimate is derived for the approximate solutions under suitable solution regularity. Numerical examples are presented to show the performance of the method.http://dx.doi.org/10.1155/S1110757X03202023 |
| spellingShingle | J. R. Fernández M. Sofonea Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage Journal of Applied Mathematics |
| title | Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage |
| title_full | Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage |
| title_fullStr | Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage |
| title_full_unstemmed | Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage |
| title_short | Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage |
| title_sort | variational and numerical analysis of the signorini s contact problem in viscoplasticity with damage |
| url | http://dx.doi.org/10.1155/S1110757X03202023 |
| work_keys_str_mv | AT jrfernandez variationalandnumericalanalysisofthesignoriniscontactprobleminviscoplasticitywithdamage AT msofonea variationalandnumericalanalysisofthesignoriniscontactprobleminviscoplasticitywithdamage |