IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Bilayer Plates: From Model Reduction to Gamma-Convergent Finite Element Approximation

  • Nov. 7, 2016
  • 1:15 p.m.
  • LeConte 312

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 consists of a geometric nonlinear fourth order problem with a nonlinear pointwise isometry constraint and 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 Kirchhoff quadrilaterals.

In this talk, we give a general overview on the model reduction procedure, discuss to 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.

Finally, we briefly discuss applications to drug delivery, which requires replacing the gradient flow relaxation by a physical flow.

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