Ricardo H. Nochetto: Local discontinuous Galerkin methods for prestrained and bilayer plates

Speaker: Ricardo H. Nochetto (University of Maryland)
Series of lectures: Research Unit 3013 Seminar
Contact: Simon Praetorius

Title
Local discontinuous Galerkin methods for prestrained and bilayer plates

Abstract
Prestrained plates are slender materials that develop internal stresses at rest, deform out of plane even without external forces, and exhibit nontrivial 3d shapes. Bilayer plates are slender structures made of two materials that react differently to environmental (thermal, electrical or chemical) actuation. In both cases the plates can exhibit large bending deformations that are geometrically nonlinear. We present reduced nonconvex models, develop variational formulations, and design local discontinuous Galerkin methods (LDGs). Moreover, we prove Gamma-convergence of the discrete energies and analyze discrete gradient flows for the computation of minimizers that provide control of the metric defect. We document the performance of the LDG methods with several insightful simulations. This is joint work with A. Bonito, D. Guignard, and S. Yang.