Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains

Kateryna Buryachenko; Annegret Glitzky; Matthias Liero; Barbara Zwicknagl

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arXiv · 2511.22320

Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains

Kateryna Buryachenko·Annegret Glitzky·Matthias Liero·Barbara Zwicknagl

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Abstract

We study the finite deformation of a thin, elastically heterogeneous sheet subject to electrostatic coupling. The interaction between mechanics and electrostatics is formulated as a saddle-point problem involving the deformation and the electrostatic potential. Starting from a three-dimensional electro-elastic model with prestrain in the elastic energy, we rigorously derive a reduced plate model in the bending regime. To perform the dimension reduction, that is, to derive the energy of a thin object by taking a suitable limit as its thickness tends to zero, we apply $Γ$-convergence-type methods to the underlying saddle-point problem. In the case of bivariate functionals, this convergence is understood in an adapted epi/hypo-convergence sense. In this concept, we demonstrate the convergence of the rescaled electro-elastic problems to an effective two-dimensional bending model coupled to electric effects. We verify that cluster points of saddle points are saddle points for the limit.

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BibTeX RIS

Kateryna Buryachenko, Annegret Glitzky, Matthias Liero, Barbara Zwicknagl. 2025-11-27. Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains. https://arxiv.org/abs/2511.22320

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