Beams are ubiquitous in our everyday life and can be found in a variety of length scales, from large supports of buildings to carbon nanotubes. Similarly, bubbles can also span a variety of scales, ranging from tiny bubbles in a glass filled with champagne to the giant soap bubbles formed by artists to attract crowds. Yet, the behavior of beams and bubbles can often occur so fast that the dynamics go unnoticed. This dissertation aims to understand the mechanics of beams and bubbles in four different examples. We combine table-top experiments with mathematical models to predict how each system will behave when exposed to different extreme conditions. We start by examining the retraction of a rubber band once it has been stretched and released. This process is similar to plucking a string, where the dynamics are governed by tensile and inertial forces, resulting in a trapezoidal shape during retraction. However when a rubber band is stretched and released, a region of high-curvature develops. Our experiments and mathematical model highlight that bending forces can be significant and give rise to a curved self-similar shape to the retracting rubber band. The next example involves the competition of surface tension and twisting on a flexible rod. Most studies in the field of elasto-capillarity have focused on how surface tension can bend an elastic structure, leaving the possibility of twisting unexplored. Here we utilize particles with discrete wettabilities -- or Janus particles -- at liquid interfaces that can be used to twist a flexible cylinder. The third system is focused around the spreading behavior of bubbles on submerged surfaces coated with a layer of oil. These liquid-infused surfaces have remarkable applications due to their ability to minimize contact line pinning. However, this property has mostly been exploited using liquid drops. We here study the early spreading behavior of a bubble once it has made contact with the liquid-infused surface. The final chapter is centered around the collapse of bubbles resting on the surface of an ultra viscous liquid. When a bubble on such a surface is ruptured, the bubble film collapses vertically downwards, leading scientists to believe that gravity is driving the collapse. Yet, interfacial forces are dominant in highly curved liquid surfaces and exceed gravitational forces. By turning the setup upside-down, we show that surface tension is indeed responsible for the collapse and the subsequent wrinkling instability that develops.

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This work focuses on understanding the buckling deformation mechanisms of bending, wrinkling, and folding that occur on the surfaces and interfaces of polymer systems. We gained fundamental insight into the formation mechanism of these buckled structures for thin glassy films placed on an elastomeric substrate. By taking advantage of geometric confinement, we demonstrated new strategies in controlling wrinkling morphologies. We were able to achieve surfaces with controlled patterned structures which will have a broad impact in optical, adhesive, microelectronics, and microfluidics applications. Wrinkles and strain localized features, such as delaminations and folds, are observed in many natural systems and are useful for a wide range of patterning applications. However, the transition from sinusoidal wrinkles to more complex strain localized structures is not well understood. We investigated the onset of wrinkling and strain localizations under uniaxial strain. We show that careful measurement of feature amplitude allowed not only the determination of wrinkle, fold, or delamination onset, but also allowed clear distinction between each feature. The folds observed in this experiment have an outward morphology from the surface in contrast to folds that form into the plane, as observed in a film floating on a liquid substrate. A critical strain map was constructed, where the critical strain was measured experimentally for wrinkling, folding, and delamination with varying film thickness and modulus. Wrinkle morphologies, i.e. amplitude and wavelength of wrinkles, affect properties such as electron transport in stretchable electronics and adhesion properties of smart surfaces. To gain an understanding of how the wrinkle morphology can be controlled, we introduced a geometrical confinement in the form of rigid boundaries. Upon straining, we found that wrinkles started near the rigid boundaries where maximum local strain occurred and propagated towards the middle as more global strain was applied. In contrast to homogeneous wrinkling with constant amplitude that is observed for an unconfined system, the wrinkling observed here had varying amplitude as a function of distance from the rigid boundaries. We demonstrated that the number of wrinkles can be tuned by controlling the distance between the rigid boundaries. Location of wrinkles was also controlled by introducing local stress distributions via patterning the elastomeric substrate. Two distinct wrinkled regions were achieved on a surface where the film is free-standing over a circular hole pattern and where the film is supported by the substrate. The hoe diameter and applied strain affected the wavelength and amplitude of the free-standing membrane. Using discontinuous dewetting, a one-step fabrication method was developed to selectively deposit a small volume of liquid in patterned microwells and encapsulate it with a polymeric film. The pull-out velocity, a velocity at which the sample is removed from a bath of liquid, was controlled to observe how encapsulation process is affected. The polymeric film was observed to wrinkle at low pull-out velocity due to no encapsulation of liquid; whereas the film bent at medium pull-out velocity due to capillary effect as the liquid evaporated through the film. To quantify the amount of liquid encapsulated, we mixed salt in water and measured the size of the deposited salt crystals. The salt crystal size, and hence the amount of liquid encapsulated, was controlled by varying either the encapsulation velocity or the size of the patterned microwells. In addition, we showed that the deposited salt crystals are protected by the laminated film until the film is removed, providing advantageous control for delivery and release. Yeast cells were also captured in the microwells to show the versatility. This encapsulation method is useful for wide range of applications, such as trapping single cells for biological studies, growing microcrystals for optical and magnetic applications, and single-use sensor technologies.

Wrinkles represent a pathway towards the spontaneous generation of ordered surface microstructure for applications in numerous fields. Examples of highly complex ordered wrinkle structures abound in Nature, but the ability to harness this potential for advanced material applications remains limited. This work focuses on understanding the relationship between the patterns on a wrinkled surface and the experimental conditions under which they form. Because wrinkles form in response to applied stresses, particular attention is given to the nature of the stresses in a wrinkling surface. The fundamental insight gained was then utilized to account for observed wrinkle formation phenomena within more complex geometric and kinetic settings. In order to carefully control and measure the applied stresses on a wrinkling film, a swelling-based system was developed using poly(dimethylsiloxane) (PDMS), surface-oxidized with a UV-ozone treatment. The swelling of the oxidized surface upon exposure to an ethanol vapor atmosphere was characterized using beam-bending experiments, allowing quantitative measurements of the applied stress. The wrinkle morphologies were characterized as a function of the overstress, defined as the ratio of the applied swelling stress to the critical buckling stress of the material. A transition in the dominant morphology of the wrinkled surfaces from dimple patterns to ridge patterns was observed at an overstress value of ~2. The pattern dependence of wrinkles on the ratio of the principal stresses was examined by fabricating samples with a gradient prestress. When swollen, these samples exhibited a smooth morphological transition from non-equibiaxial to equibiaxial patterns, with prestrains as low as 2.5% exhibiting non-equibiaxial characteristics. This transition was seen both in samples with low and high overstresses. To explore the impact of these stress states in more complex geometries, wrinkling hemispherical surfaces with radii of curvature ranging from 50-1000 μm were fabricated using the same material system. Upon wrinkling, the hemispheres formed complex hierarchical assemblies reminiscent of naturally occurring structures. The curvature of a surface exhibited a correlation with its critical buckling stress, independent of other factors. This enables the surface curvature to be used as an independent control over the dimple-to-ridge transition which occurs as a function of overstress. As in the flat buckling surfaces, this transition was shown to occur at an overstress value of ~2. Surface curvature was also shown to improve the observed hexagonal ordering of the dimple arrays, resulting in the formation of regular "golf ball" structures. Geometric effects in finite flat plates were also examined. Using circular masks during the oxidation process, plates with radii ranging from 0.4-8.6 mm were created. Upon wrinkling, a dimple-to-ridge transition was observed with increasing plate size, with the morphological switch occurring at a radius of ~2 mm. This observed transition was not found to be due to the inherent mechanics of plates of different sizes, but instead to a reduction in the oxide conversion due to shadowing or stagnation caused by the masking process, which lowered the applied overstress. The shape of the finite plate was found to have little impact on the resulting wrinkle morphologies. Kinetic aspects of wrinkling were qualitatively characterized by observing the wrinkling process over the course of swelling. Wrinkling was observed to frontally propagate across the surface, and the ordering of the patterns which developed showed a qualitative correlation with the degree of uniformity in the advancing wrinkle front. Swelling with different solvents was found to lead to the formation of different patterns, based on the swelling kinetics of the UVO-treated PDMS upon exposure to each solvent.

The applications of membranes are increasing rapidly in various fields of engineering and science. The geometric, material, force and contact non-linearities complicate their analysis, which increases the demand for computationally efficient methods and interpretation of counter-intuitive behaviours. The first part of the present work studies the free and constrained inflation of circular and cylindrical membranes. The membranes are assumed to be in contact with a soft substrate, modelled as a linear spring distribution.Adhesive and frictionless contact conditions are considered during inflation,while only adhesive contact conditions are considered during deflation. For a circular membrane, peeling of the membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed. The second part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Limit points and bifurcation points are observed on primary equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by eigenvectors corresponding to zero eigenvalues at the bifurcation point. Symmetry has major implications on stability analysis of the structures, and the relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis. In the third part, wrinkling in the pressurized membranes is investigated,and robustness of the modified membrane theory and tension field theory is examined. The effect of boundary conditions, thickness variations, and inflating media on the wrinkling is investigated. It is observed that, with a relaxed strain energy formulation, the obtained equilibrium solutions are unstable due to the occurrence of pressure induced instabilities. A detailed analysis of pressure induced instabilities in the wrinkled membranes is described in the thesis. / <p>QC 20160518</p>

Das Formdrücken findet seine industrielle Anwendung in der Herstellung rotationssymmetrischer Hohlbauteile für kleine und mittlere Losgrößen. Diese Bauteile werden häufig in einem weiteren Verfahrensschritt als Vorform für die Herstellung profilierter Hohlkörper genutzt. Verfahrensbedingt tritt bereits bei der Vorformherstellung eine ungewollte Blechdickenabnahme auf. Um diese Blechdickenabnahme zu minimieren, wurde anhand numerischer Methoden das Verfahren des Rotationsschwenkbiegens an der Professur Virtuelle Fertigungstechnik der TU Chemnitz entwickelt. Das Prinzip dieses inkrementellen Umformprozesses basiert auf einer Verfahrenskombination des konventionellen Drückens und des Schwenkbiegens, mit dem Ziel der faltenfreien Herstellung von Hohlbauteilen bei gleichzeitiger minimaler Blechausdünnung. Die als Halbzeug verwendete Ronde wird zu Beginn des Prozesses auf eine formgebende Matrize gespannt und in Rotation versetzt. Durch die Schwenkbewegung eines zylindrischen Umformwerkzeuges wird das ebene Blech an die Kontur der Matrize angelegt, wobei keine Relativbewegung zwischen Blech und Werkzeug stattfindet. Demzufolge entstehen minimale Zugspannungen in der Blechebene und die Blechausdünnung wird deutlich verringert. Durch die Durchmesserreduzierung bilden sich jedoch ebenso tangentiale Druckspannungen aus, welche zu einer ungewollten Faltenbildung führen können. Im Rahmen des Vortrages werden anhand von FEM-Simulationen Möglichkeiten vorgestellt, um diese Druckspannungen zu reduzieren oder gezielt zur Vorformherstellung für profilierte Hohlbauteile zu nutzen.

Deep drawing operations are crucial for metal forming operations and manufacturing. Obtaining a defect free final product with the desired mechanical properties is very important for fulfilling the customer expectations and market competitions. Wrinkling is one of the fatal and most frequent defects that must be prevented. This study focuses on understanding the phenomenon of wrinkling and probable precautions that can be applied. In this study, dynamic &ndash / explicit commercial finite element code is used to simulate deep drawing process. The numerical experiments are compared with NUMISHEET benchmarks in order to verify the reliability of the finite element code and analysis parameters. In order to understand plastic wrinkling, the effect of blank holder force is investigated. Axisymmetrical numerical models of a cup are investigated with different blank holder forces. Wrinkling instability is illustrated in energy diagrams of the process. Effect of anisotropy on wrinkling is also discussed by comparing isotropic and anisotropic numerical experiments with the material as steel. Different drawbead models, both equivalent and physical, are implied to the problem and results are discussed. Besides numerical analysis, experimental verification is also conducted as conventional deep drawing operation by a hydraulic press. This yields to the ability to understand the effect of blank thickness on wrinkling formation through numerical and experimental analyses. The wave formations of different sized blanks with four different thicknesses are illustrated.

In several practical applications, hot-finished steel pipe that exhibits Lüders bands is bent to strains of 2-3%. Lüders banding is a material instability that leads to inhomogeneous plastic deformation in the range of 1-4%. This work investigates the influence of Lüders banding on the inelastic response and stability of tubes under rotation controlled pure bending. It starts with the results of an experimental study involving tubes of several diameter-to-thickness ratios in the range of 33.2 to 14.7 and Lüders strains of 1.8% to 2.7%. In all cases, the initial elastic regime terminates at a local moment maximum and the local nucleation of narrow angled Lüders bands of higher strain on the tension and compression sides of the tube. As the rotation continues, the bands multiply and spread axially causing the affected zone to bend to a higher curvature while the rest of the tube is still at the curvature corresponding to the initial moment maximum. With further rotation of the ends, the higher curvature zone(s) gradually spreads while the moment remains essentially unchanged. For relatively low D/t tubes and/or short Lüders strains, the whole tube eventually is deformed to the higher curvature entering the usual hardening regime. Subsequently it continues to deform uniformly until the usual limit moment instability is reached. For high D/t tubes and/or materials with longer Lüders strains, the propagation of the larger curvature is interrupted by collapse when a critical length is Lüders deformed leaving behind part of the structure essentially undeformed. The higher the D/t and/or the longer the Lüders strain is, the shorter the critical length. This class of problems is analyzed using 3D finite elements while the material is modeled as an elastic-plastic solid with an “up-down-up” response over the extent of the Lüders strain, followed by hardening. The analysis reproduces the main features of the mechanical behavior provided the unstable part of the response is suitably calibrated. The uniform curvature elastic regime terminates with the nucleation of localized banded deformation. The bands appear in pockets on the most deformed sites of the tube and propagate into the hitherto intact part of the structure while the moment remains essentially unchanged. The Lüders-deformed section has a higher curvature, ovalizes more than the rest of the tube, and develops wrinkles with a characteristic wavelength. For every tube D/t there exists a threshold of Lüders strain separating the two types of behavior. This bounding value of Lüders strain was studied parametrically. / text

COMPUTER AIDED MODELING OF WRINKLING AND ITS PREVENTION PiSKiN, Mehmet Ali M.S., Department of Mechanical Engineering Supervisor: Prof. Dr. Bilgin KAFTANOgLU September 2005, 111 Pages Deep-drawing operations are performed widely in industrial applications. It is very important for efficiency to achieve parts with no defects. Wrinkling is a kind of defect caused by stresses in the flange part of the blank during metal forming operations. It is required that the flange of a workpiece in deep drawing operation should deform in its plane without wrinkling otherwise it will impair the quality of the product. To avoid wrinkling appropriate blank-holder force or drawbead can be applied. In this work, finite element method is used to obtain the wrinkling behavior. A four nodded five degree of freedom shell element is formulated. Isotropic elasto-plastic material model with Von Mises yield criterion is used. By using this shell element, the developed code can predict the bending behavior of workpiece besides membrane behavior. Simulations are carried out with four different element sizes and two different shapes (circular and rectangular). The thickness strain and nodal displacement values obtained are compared with results of a commercial finite element program and results of previously conducted experiments.