[PhD Thesis Public Presentation_Zoom] ‐ Alexandru Mihai– “ Soap film mediated 3D Self-Assembly: Suspended and Displacement Driven Geometries using centimeter-scale tiles”
Presenter: Alexandru Mihai
Supervisor: Prof. Eliot Fried
Unit: Mechanics and Materials Unit
Zoom URL: to be available 48 hours prior to the examination
Title: Soap film mediated 3D Self-Assembly: Suspended and Displacement Driven Geometries using centimeter-scale tiles
The self-assembly of polygonal pieces within a soap film is demonstrated. Gravity mediated as well as displacement driven assemblies of polygonal frames within a soap film are shown, namely five (platonic solid) geometries and 24 free-standing structures respectively. A model of axes-symmetric geometries is presented and compared to experimental results of 3D printed rings solely supported by a soap film membrane counteracting the gravitational force acting on the rings. The model is derived by both energy methods (using a calculus of variations approach) and a direct force balance approach. The explicit solution of the system extends the Goldschmidt limit of catenoid shaped minimal surfaces to include load bearing geometries corresponding to the maximal mass supported by a soap film spanning two rings of given radius. This model provides an approximation of the self-assembled polygonal frames suspended in the soap film. Computational results using the FEniCS Project package confirm the analytical results for axes-symmetric and one-dimensional geometries. Eight prism and 16 pyramidal structures of varying base geometry and heights are constructed through a displacement driven approach on a base plate by the smooth deformation of a catenoid-like soap film until the film is no longer stable, resulting in a pinch-off phenomenon. Coupled with the edge-to-edge alignment of polygonal frames the pinch-off of the membrane results in free standing prism, pyramid, and octahedral geometries. Two effective radii corresponding to prism and pyramid structures respectively are derived, and found to predict the separation between the base and support needed for the pinch-off of the soap film to occur.