Local discontinuous Galerkin methods for prestrained and bilayer plates

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.