Fine Properties and Applications of Thin-Sheet Folding

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In the first funding period of the research project, the analytical understanding and the reliable numerical approximation of thin-sheet folding processes have been addressed. In particular, a two-dimensional bending-folding model has been derived from a three-dimensional hyper-elastic material description of a pre-damaged plate, a discontinuous Galerkin method has been devised, quasi-optimal error estimates for a corresponding small deflection interface problem have been established, and a precise characterization of the relation of folding angles and curvature quantities along creases has been identified. Further results are subject of ongoing research. In a second funding period specific analytical questions such as the optimality of scaling relations leading to other interface conditions, the understanding of piecewise smooth folding line systems, and the characterization of folding angle discontinuities will be addressed. Besides this, the improvement of the efficiency of basic numerical schemes via acceleration procedures and adaptive local mesh refinement based on a posteriori error estimates will be analyzed. Using the analytical results and new computational methodology, application-related questions including the leverage effect of different folding constructions, the development of new mechanisms based on singular flapping effects, and the determination of unstable critical configurations arising in switching processes of bistable devices will be investigated.