SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2016-2017



Jeudi 24 novembre 2016 : Ricardo H. NOCHETTO (Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, United States)
Bilayer Plates: Model Reduction, Discretization and Gradient Flow



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 in this talk, consists of a nonlinear fourth order problem with a pointwise isometry constraint. A discretization based on Kirchhoff quadrilaterals is devised and its $\Gamma$-convergence is proved. A discrete gradient flow 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. This is joint work with S. Bartels and A. Bonito.