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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universidade Federal de Viçosa (UFV)
2024-10-01
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| Series: | The Journal of Engineering and Exact Sciences |
| Subjects: | |
| Online Access: | https://periodicos.ufv.br/jcec/article/view/19419 |
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| Summary: | 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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| ISSN: | 2527-1075 |