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Penalization of Coulomb’s frictional Signorini’s contact problem for locking piezoelectric materials

期刊论文
发表日期：

2025年5月30日

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Hamid El Khalfi,
Hicham Benaissa

摘要

We apply here a penalization method to a Coulomb’s frictional contact problem in locking piezoelectric materials. We first present the mathematical model for our static frictional electro-elastic contact process, we then derive its weak formulation in terms of the displacement and electric potential fields, and we establish the unique solvability of the derived variational problem. Secondly, we consider a penalized weak problems in the form of variational equalities where the constitutive laws and Signorini’s contact conditions are regularized. Then, we prove the existence and uniqueness of the continuous penalized solution and its convergence as the penalty parameter tends to zero. Finally, the finite element discretized penalty method is analyzed, along with a review of related convergence results. Notice that different estimates depending on the mesh size $\textbf{h}$ $h$ and $\varepsilon $ $ε$ are obtained, and the theoretical convergence of the penalization method produces the finest results when $\varepsilon = 1/\textbf{n}$ $ε = 1 / n$ and $\textbf{h}= 1/\textbf{n}^{2}$ $h = 1 / n^{2}$ .