Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory
We investigate a mathematical problem involving dynamic interaction between a viscoelastic body with long-term memory loss and an obstruction. The contact is frictional and bilateral, with a moving rigid base, resulting in wear of the contacting surface. The problem is expressed as a coupled system...
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| Format: | Article |
| Language: | English |
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Universidade Federal de Viçosa (UFV)
2024-10-01
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| Series: | The Journal of Engineering and Exact Sciences |
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| Online Access: | https://periodicos.ufv.br/jcec/article/view/19419 |
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| author | Ahmed Hamidat Hakim Bagua Adel Aissaoui |
| author_facet | Ahmed Hamidat Hakim Bagua Adel Aissaoui |
| author_sort | Ahmed Hamidat |
| collection | DOAJ |
| description |
We investigate a mathematical problem involving dynamic interaction between a viscoelastic body with long-term memory loss and an obstruction. The contact is frictional and bilateral, with a moving rigid base, resulting in wear of the contacting surface. The problem is expressed as a coupled system, with a hyperbolic quasi-variational inequality for displacement and a parabolic variational inequality for damage. We define a variational formulation for the model and demonstrate the existence of a single weak solution to the problem. The material behaviour is explained using a viscoelastic constitutive law that includes long-term memory and damage. Elastic deformations induce material deterioration, which is depicted by a parabolic inclusion. The proof is based on classical existence.
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| format | Article |
| id | doaj-art-eaf13afbcb164646895d3dfd7561e49e |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-eaf13afbcb164646895d3dfd7561e49e2025-02-02T19:53:22ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752024-10-0110610.18540/jcecvl10iss6pp19419Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term MemoryAhmed Hamidat0Hakim Bagua1Adel Aissaoui2Laboratory of Operator Theory and PDE: Foundations and Applications, University of El Oued, AlgeriaDepartment of Electronics and Telecommunication, Faculty of New Technologies of Information and Communication, University of Ouargla, AlgeriaLaboratory of Operator Theory and PDE: Foundations and Applications, University of El Oued, Algeria We investigate a mathematical problem involving dynamic interaction between a viscoelastic body with long-term memory loss and an obstruction. The contact is frictional and bilateral, with a moving rigid base, resulting in wear of the contacting surface. The problem is expressed as a coupled system, with a hyperbolic quasi-variational inequality for displacement and a parabolic variational inequality for damage. We define a variational formulation for the model and demonstrate the existence of a single weak solution to the problem. The material behaviour is explained using a viscoelastic constitutive law that includes long-term memory and damage. Elastic deformations induce material deterioration, which is depicted by a parabolic inclusion. The proof is based on classical existence. https://periodicos.ufv.br/jcec/article/view/19419Viscoelastic. Long-term memory. Wear. Damage. Fixed point. Hyperbolic. Quasi-variational inequality. |
| spellingShingle | Ahmed Hamidat Hakim Bagua Adel Aissaoui Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory The Journal of Engineering and Exact Sciences Viscoelastic. Long-term memory. Wear. Damage. Fixed point. Hyperbolic. Quasi-variational inequality. |
| title | Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory |
| title_full | Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory |
| title_fullStr | Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory |
| title_full_unstemmed | Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory |
| title_short | Variational Analysis of a Dynamic Contact Problem with Wear and Damage Involving Viscoelastic Materials with Long-Term Memory |
| title_sort | variational analysis of a dynamic contact problem with wear and damage involving viscoelastic materials with long term memory |
| topic | Viscoelastic. Long-term memory. Wear. Damage. Fixed point. Hyperbolic. Quasi-variational inequality. |
| url | https://periodicos.ufv.br/jcec/article/view/19419 |
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