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Mechanics of thin films: simulation of some nonlinear PDE – running

Wrinkling is a buckling phenomenon, typical on thin (a few micrometer thick) films. It can occur not only as a result of overall compression but also because of shear or tensile forces. The aim of this project is to investigate the role of the boundary conditions and some other parameters influencing the wrinkled profiles and patterns by numerical simulations based on the Föppl- von Kármán plate theory and simultaneous experiments. Stability of the solutions is a key question as the problem is highly nonlinear. Accordingly bifurcation points of the equilibrium path and stability regions should be determined.
The mechanical approach is a recent extension of the Föppl- von Kármán theory assuming large in plane elongations and material nonlinearities. The limits of the application of both the Föppl- von Kármán theory and its extended counterpart are far not clear. Beyond mathematical considerations, numerical and experimental results could also help to gain deeper understanding.
Simple simulations of the extended model are in good agreement with the experimental results, however the high computational need of the calculations limits the explorable parameter range. The numerical simulations aimed at the super computer are based on the Discontinuous Galerkin method, which provides the sufficient continuity for fourth order problems via finites elements possessing C0 and C1 continuity (instead of C2 elements). The proposed program is based on FEniCS, an open-source finite element software. Bifuraction points of the equilibrium path and stability regions are determined by a newly developed continuation procedure.

Project owner:
Fehér Eszter (Szilárdságtani és Tartószerkezeti Tanszék)
Members:
Szilárdságtani és Tartószerkezeti Tanszék (ÉPK-SZT)