Premium
Bilayer Plates: Model Reduction, Γ‐Convergent Finite Element Approximation, and Discrete Gradient Flow
Author(s) -
Bartels Sören,
Bonito Andrea,
Nochetto Ricardo H.
Publication year - 2017
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21626
Subject(s) - mathematics , discretization , pointwise , finite element method , nonlinear system , isometry (riemannian geometry) , mathematical analysis , convergence (economics) , physics , quantum mechanics , economics , thermodynamics , economic growth
The bending of bilayer plates is a mechanism that 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 Γ‐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.© 2015 Wiley Periodicals, Inc.