A Decomposition Method for a Unilateral Contact Problem with Tresca Friction Arising in Electro-elastostatics |
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Authors: | E-H Essoufi R Fakhar |
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Institution: | 1. Laboratory of Mathematics, Informatics and Engineering (MISI), University Hassan 1st, Setttat, Morocco;2. Laboratory of Material Sciences, Medium and Modelling (LS3?M), University Hassan 1st, Khourigba, Morocco |
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Abstract: | This article is concerned with the numerical modeling of unilateral contact problems in an electro-elastic material with Tresca friction law and electrical conductivity condition. First, we prove the existence and uniqueness of the weak solution of the model. Rather than deriving a solution method for the full coupled problem, we present and study a successive iterative (decomposition) method. The idea is to solve successively a displacement subproblem and an electric potential subproblem in block Gauss-Seidel fashion. The displacement subproblem leads to a constraint non-differentiable (convex) minimization problem for which we propose an augmented Lagrangian algorithm. The electric potential unknown is computed explicitly using the Riesz's representation theorem. The convergence of the iterative decomposition method is proved. Some numerical experiments are carried out to illustrate the performances of the proposed algorithm. |
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Keywords: | Augmented Lagrangian Electro-elastostatics Signorini contact problem Tresca friction |
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