The present paper is devoted to the study a dynamic problem describing a frictionless contact between a thermo- elasto-viscoplastic body and an adhesive foundation. The constitutive law includes a temperature effect described by the first order evolution equation. The contact is modelled with a normal compliance condition involving adhesion effect of contact surfaces. The adhesion is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. A variational formulation for the problem is given as a system involving the displacement field, the bonding field and the temperature field. The existence and the uniqueness of the weak solution are established. The proof is based on evolution equation with monotone operators, differential equations and fixed point theorem.
| Published in | Mathematical Modelling and Applications (Volume 9, Issue 1) |
| DOI | 10.11648/mma.20240901.11 |
| Page(s) | 1-13 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Thermo-elasto-viscoplastic Materials, Dynamic Process, Frictionless Contact, Normal Compliance, Adhesion, Weak Solution, Ordinary Differential Equation, Evolution Equation, Fixed Point
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APA Style
Selmani, M. (2024). A Dynamic Frictionless Contact Problem with Adhesion in Thermo-elasto-viscoplasticity. Mathematical Modelling and Applications, 9(1), 1-13. https://doi.org/10.11648/mma.20240901.11
ACS Style
Selmani, M. A Dynamic Frictionless Contact Problem with Adhesion in Thermo-elasto-viscoplasticity. Math. Model. Appl. 2024, 9(1), 1-13. doi: 10.11648/mma.20240901.11
AMA Style
Selmani M. A Dynamic Frictionless Contact Problem with Adhesion in Thermo-elasto-viscoplasticity. Math Model Appl. 2024;9(1):1-13. doi: 10.11648/mma.20240901.11
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Download@article{10.11648/mma.20240901.11,
author = {Mohamed Selmani},
title = {A Dynamic Frictionless Contact Problem with Adhesion in Thermo-elasto-viscoplasticity},
journal = {Mathematical Modelling and Applications},
volume = {9},
number = {1},
pages = {1-13},
doi = {10.11648/mma.20240901.11},
url = {https://doi.org/10.11648/mma.20240901.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.mma.20240901.11},
abstract = {The present paper is devoted to the study a dynamic problem describing a frictionless contact between a thermo- elasto-viscoplastic body and an adhesive foundation. The constitutive law includes a temperature effect described by the first order evolution equation. The contact is modelled with a normal compliance condition involving adhesion effect of contact surfaces. The adhesion is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. A variational formulation for the problem is given as a system involving the displacement field, the bonding field and the temperature field. The existence and the uniqueness of the weak solution are established. The proof is based on evolution equation with monotone operators, differential equations and fixed point theorem.},
year = {2024}
}
TY - JOUR T1 - A Dynamic Frictionless Contact Problem with Adhesion in Thermo-elasto-viscoplasticity AU - Mohamed Selmani Y1 - 2024/02/05 PY - 2024 N1 - https://doi.org/10.11648/mma.20240901.11 DO - 10.11648/mma.20240901.11 T2 - Mathematical Modelling and Applications JF - Mathematical Modelling and Applications JO - Mathematical Modelling and Applications SP - 1 EP - 13 PB - Science Publishing Group SN - 2575-1794 UR - https://doi.org/10.11648/mma.20240901.11 AB - The present paper is devoted to the study a dynamic problem describing a frictionless contact between a thermo- elasto-viscoplastic body and an adhesive foundation. The constitutive law includes a temperature effect described by the first order evolution equation. The contact is modelled with a normal compliance condition involving adhesion effect of contact surfaces. The adhesion is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. A variational formulation for the problem is given as a system involving the displacement field, the bonding field and the temperature field. The existence and the uniqueness of the weak solution are established. The proof is based on evolution equation with monotone operators, differential equations and fixed point theorem. VL - 9 IS - 1 ER -
Department of Mathematics, Setif 1 University-Ferhat Abbas, Setif, Algeria
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