- AutorIn
- Lisa Julia Nebel Technische Universität Dresden, Institut für Numerische Mathematik
- Titel
- Formation of wrinkles on a coated substrate
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-887051
- Erstveröffentlichung
- 2023
- Datum der Einreichung
- 02.08.2023
- Datum der Verteidigung
- 08.12.2023
- Abstract (EN)
- The dissertation “Formation of wrinkles on a coated substate“ treats the finite element simulations of controlled wrinkle formation experiments conducted at the Leibniz Institute for Polymer Research. The systems used for the experiments consist of a soft polydimethylsiloxane (PDMS) layer with a thin, stiff layer on top. The wrinkling process is triggered by a stress mismatch between the bulk and the thin layer. To create the stress mismatch, the bulk material is first uni-axially stretched and then the thin layer is created by a low-pressure plasma treatment of the stretched bulk in a vacuum chamber. Under subsequent relaxation, wrinkles form. Their wavelength depends on the choice of the process gas and the duration of the treatment. The use of thin silicon masks placed directly on the PDMS allows to sharply restrict the plasma-exposed area. Sequential exposures of the same sample to multiple treatment processes with and without a mask allow to locally modify the layer thickness and stiffness. With this, we can locally control the wavelength of the resulting wrinkles and trigger the formation of branches and line defects at the boundary between areas of different wavelengths. The dissertation first covers the mathematical model for the coated substrate, a combination of a hyperelastic material model from three-dimensional elasticity for the bulk (an almost incompressible Mooney–Rivlin material model) and a Cosserat shell model for the film on top. A nonlinear and nonconvex minimization problem is deduced and transferred to a suitable finite element space. Existence of minimizers is proven in the continuous and the discrete case before the discrete problem is solved numerically. The numerical simulations show a good agreement with corresponding physical experiments.
- Verweis
- Controlling line defects in wrinkling: a pathway towards hierarchical wrinkling structures
DOI: 10.1039/d0sm02231d - Formation of wrinkles on a coated substrate using manifold‐valued finite elements
DOI: 10.1002/pamm.202300072 - Freie Schlagwörter (EN)
- bulk-shell coupling, elastic shell, Cosserat shell, geometrically nonlinear, geometric finite elements
- Klassifikation (DDC)
- 510
- Klassifikation (RVK)
- SK 910
- SK 950
- GutachterIn
- Prof. Dr. Oliver Sander
- Assoz.Univprof. Dr. Astrid Pechstein
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Dresden, Dresden
- Förder- / Projektangaben
- Deutsche Forschungsgemeinschaft ID: SA 2130/6-1
- Version / Begutachtungsstatus
- aktualisierte Version
- URN Qucosa
- urn:nbn:de:bsz:14-qucosa2-887051
- Veröffentlichungsdatum Qucosa
- 18.12.2023
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
- CC BY 4.0