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.
