Bilayer Plates: Model Reduction, Γ-Convergent Finite Element Approximation, and Discrete Gradient Flow
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Publication:2965551
DOI10.1002/CPA.21626zbMATH Open1357.74029arXiv1506.03335OpenAlexW2964065979MaRDI QIDQ2965551
Author name not available (Why is that?)
Publication date: 3 March 2017
Published in: (Search for Journal in Brave)
Abstract: The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order problem with a pointwise isometry constraint. A discretization based on Kirchhoff quadrilaterals is devised and its -convergence is proved. An iterative method that decreases the energy is proposed and its convergence to stationary configurations is investigated. Its performance, as well as reduced model capabilities, are explored via several insightful numerical experiments involving large (geometrically nonlinear) deformations.
Full work available at URL: https://arxiv.org/abs/1506.03335
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