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217 personnes travaillent au LJLL

83 personnels permanents

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Chiffres janvier 2014

 

Séminaire du LJLL - 08 06 2018 14h00 : A. Bonito

Andrea Bonito (Université A&M du Texas, College Station)

Bilayer plates : from model reduction to Gamma-convergent finite element approximation

Résumé
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 consists of a geometric nonlinear fourth order problem with a nonlinear pointwise isometry constraint where the lattice mismatches act as a spontaneous curvature. A gradient flow is proposed to decrease the system energy and is coupled with finite element approximations of the plate deformations based on either Kirchhoff or discontinuous Galerkin finite elements.
In this talk, we give a general overview on the model reduction procedure, discuss the convergence of the iterative algorithm towards stationary configurations and the Gamma-convergence of their finite element approximations. We also explore the performances of the numerical algorithm as well as the reduced model capabilities via several insightful numerical experiments involving large (geometrically nonlinear) deformations.