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Research Article |

A Dynamic Frictionless Contact Problem with Adhesion in Thermo-elasto-viscoplasticity

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.

Thermo-elasto-viscoplastic Materials, Dynamic Process, Frictionless Contact, Normal Compliance, Adhesion, Weak Solution, Ordinary Differential Equation, Evolution Equation, Fixed Point

APA Style

Selmani, M. (2024). A Dynamic Frictionless Contact Problem with Adhesion in Thermo-elasto-viscoplasticity. Mathematical Modelling and Applications, 9(1), 1-13.

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

Copyright © 2024 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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