Date of Award
5-11-2025
Date Published
June 2025
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Physics
Advisor(s)
Joseph Paulsen
Subject Categories
Condensed Matter Physics | Physical Sciences and Mathematics | Physics
Abstract
Soft reconfigurable systems exhibit behaviors which are highly dependent on their geometries. Thin membranes can deform in a myriad of ways as they navigate geometries different from their own in an energy efficient manner. Behaviors in mechanical hysteron systems are influenced by the geometry of the interactions and global driving. This dissertation focuses on two different types of systems which are governed in part by their geometries: thin membranes in geometrically incompatible configurations and interacting mechanical hysterons. A thin membrane forced into a conflicting geometry with an incompatible metric will deform in highly non-trivial ways. These deformations are an attempt by the system to select the most energetically-favorable configuration. In confined inflated bag systems, we observe a transition from sharp (crumples) to smooth (wrinkles) deformations which depend on the curvature of the system. We find crumples have localized regions of high Gaussian curvature, indicating high material stress, and wrinkles to have more spatially extended and less localized Gaussian curvatures. We also analytically, numerically, and experimentally study the shape of a thin membrane on a liquid interface where both the membrane and interface are highly deformable. We find the sheet take a cylindrical shape for surfaces of negative Gaussian curvature and adopts a cylindrical inner region for surfaces of positive Gaussian curvature. The Preisach model, which has successfully described phenomenon such as ferromagnetism in materials, utilizes non-interacting hysterons as the basic units of this hysteresis. This model can be extended to include interactions between the hysterons which allow us to unlock new and complex behaviors. We study a mechanical hysteron system of rotors composed of rigid bars which can rotate between two hard boundaries. These rotors are coupled together with springs and experience a horizontal global driving via a spring connected to a bar. We find a variety of interesting responses which arise from the underlying geometry of these connections.
Access
Open Access
Recommended Citation
Schrecengost, Zachariah, "Deformations of thin membranes in incompatible geometries and interactions in mechanical hysteron systems" (2025). Dissertations - ALL. 2108.
https://surface.syr.edu/etd/2108
