Date of Award

Winter 12-22-2021

Degree Type


Degree Name

Doctor of Philosophy (PhD)




Paulsen, Joseph

Second Advisor

Zhang, Teng


Buckling, Crumpling, Elastic, instability, Interfacial, Thin Film

Subject Categories

Physical Sciences and Mathematics | Physics


Thin elastic solids are easily deformed and will readily collapse into complex buckling modes. They can also transition between distinct buckling modes when the confining forces evolve over time, forming a variety of robust and striking patterns. Here we explore how thin interfacial films and the buckling modes they present couple with evolving macroscopic forces and how multi-scale features of the systems give rise to patterns.

In the indentation of a circular film floating on a liquid bath three buckling modes arise: wrinkling, crumpling, and folding. This work shows that striking transitions between these states accompany four regimes in the force of indentation, two of which represent nonlinear responses to this loading. I use high precision force measurements to confirm a recently predicted[Vella et al. 2018] stiffening response and further identify a softening response at large slopes. These non-linearities are shown to arise from purely geometrical effects that modify the stress field and film profile. We harness this same experimental setup to characterize the threshold for the formation of folds; regions where material spontaneously localizes and contacts itself. We show that a previous scaling argument for the onset of folds does not describe our data, and we investigate other possible scalings with system parameters.

Next, we turn to ask how a wrinkled film may couple to the forces that it exerts on its surroundings. I show that a mismatch in curvature between a film and a liquid meniscus can in general cause it to experience a net force along the liquid surface. I release thin polymer films from different locations on an interface with both nominally flat areas and areas of high curvature and measure the spontaneous migration velocity curve. By isolating this effect in two curvature settings, singly and doubly curved surfaces, I demonstrate that the effect is created by surface area modulation caused by complex buckling rather than the elastic energies of the sheet. This implies that geometric incompatibility gives rise to this phenomenon which is reinforced by the observation that flat films and curved films will flee areas of dissimilar geometry for those of similar geometry.

While the wrinkle wavelength in interfacial films is known to be a micro-scale feature set by a balance of the film bending rigidity and substrate stiffness, the crumpling mode is comparatively less understood. I contribute measurements of robust morphological features of crumpling in the interfacial indentation setting to a broad study of crumples in varied geometries and boundary conditions. We construct an empirical phase diagram of the wrinkle-to-crumple transition which suggests crumples are a generic micro-structure that emerges at large curvatures due to a competition of elastic and substrate energies.

Finally, I present high contrast images of large area films to uncover a new "defect-rich" regime. We construct a phase diagram capturing the transition between these two states and show that the new regime features "smectic" regions of constant wavelength, radially oriented wrinkles where both the micro and macro-scale features are satisfied. This is facilitated by frustrated "defect" regions where wrinkles are inserted which causes local deviation from radial orientation and preferred wavelength.


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