Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session S25: Shell Buckling |
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Sponsoring Units: GSNP Chair: Shmuel Rubinstein, Harvard University Room: 402 |
Thursday, March 5, 2020 11:15AM - 11:51AM |
S25.00001: TBD Invited Speaker: Ousmane Kodio tbd |
Thursday, March 5, 2020 11:51AM - 12:03PM |
S25.00002: Postbuckling analysis of hyperelastic thick tube Yu Zhou, Yuzhen Chen, Lihua Jin In recent years, mechanical instabilities of soft materials have been substantially investigated and utilized. Though tube structures are widely used and instabilities of thin-walled tubes are well studied, postbuckling behavior of hyperelastic thick tubes is elusive. It is well known that exact solutions of postbuckling are hard to obtain, especially for structures under three-dimensional finite deformation. In this presentation, we conduct buckling and postbuckling analysis for hyperelastic thick tubes undergoing finite deformation. We will briefly introduce the asymptotic expansion method for buckling and weakly postbuckling of elastic bodies and apply this theory to thick tubes. Our analytical results are validated by finite element simulations. As a result, a long tube prefers the Euler buckling mode, while a short tube prefers the barreling mode. Depending on the geometry, three kinds of postbuckling paths, including increasing force, snap-through and snap-back, are discovered. We summarize our results in two phase diagrams of buckling and postbuckling with respect to geometric parameters, which provide guidelines for utilization of tube structures. |
Thursday, March 5, 2020 12:03PM - 12:15PM |
S25.00003: Buckling in thin thermalized ribbons under longitudinal compression Paul Hanakata, Abigail Plummer, Suraj Shankar, David Robert Nelson Introducing kirigami cuts to thin sheets, ranging from macro to nanoscale, can allow for sensitive control of mechanical properties such as stretchability. The out-of-plane buckling due to in-plane compression can be a key feature in preventing failure upon stretching. While thin plate theory can predict critical buckling for thin frames and nanoribbons at very low temperatures, a unifying framework to describe the effects of thermal fluctuations on the buckling presents subtle problems. In analogy with understanding semi-flexible polymers with long persistence lengths, we address under what conditions a thin thermalized nanoribbon behaves like a classical plate and how its thermal modes compete with the buckling modes. We develop a mean field approach to understand how the critical buckling changes due to thermal fluctuations both above and below the buckling transition. We simulate thin graphene nanoribbons under axial compression using molecular dynamics simulations to test our predictions. |
Thursday, March 5, 2020 12:15PM - 12:27PM |
S25.00004: Poking and buckling of pressurized spherical shells Arefeh Abbasi, Dong Yan, Matteo Pezzulla, Pedro Reis Imperfection sensitivity in shell buckling makes it difficult to predict the critical buckling conditions of shells with realistic distributions of defects. Recently, a non-destructive technique has been proposed and successfully applied to cylindrical shells [1,2], to access their landscape of stability using a probing force. It is still debatable whether this technique can also be used for spherical shells. Here, we combine precision experiments, finite element simulations and shell theory to explore the ability of a poking technique to determine the critical buckling pressure of a spherical shell containing a dimple-like defect. We find that the critical point can indeed be probed when the force is applied at the defect. However, when the poking is done further away from the defect, this becomes invisible to the probing and the shell buckles prior to the cue provided by the poking. Specifically, we quantify a threshold angle for the location of the probing force, beyond which poking no longer seems to be applicable as a non-destructive testing technique. The basis of our analysis is the localized nature of the deformation of shells under point-load indentation. |
Thursday, March 5, 2020 12:27PM - 12:39PM |
S25.00005: Multi-component assembly of microcompartments Siyu Li, Yaohua Li, Taylor Nichols, Nolan Kennedy, Danielle Tullman-Ercek, Monica Olvera De La Cruz Many bacteria generate bacterial microcompartments (BMC) in their metabolic processes. These particles are protein-based shells that encapsulate enzymes spontaneously. Using all-atom and coarse-grained molecular dynamics, we study the mechanical properties of protein subunits and the assembly process. We find that the hexamers (PduA) are associated mainly due to the hydrogen bonding, the strength of which exactly corresponds to the region that BMC successfully formed. In addition, we observe cylinder and “samosa” shaped shells coexistent in solution when reducing the pentamer (PduN)-hexamer interaction. We calculate the free energy for each morphology thermodynamically and find that the cargo-hexamer attraction in cylinder/samosa compensates the energy loss of missing pentamers. We also discuss other thermodynamic parameters that can be used to control the shell morphology, which provides a prediction for future experiments. |
Thursday, March 5, 2020 12:39PM - 12:51PM |
S25.00006: Shallowness effect on buckling of spherical shells Kanghyun Ki, Jeongrak Lee, Anna Lee We study the buckling of clamped spherical caps under uniform pressure. Since the 1960s, several theoretical and computational studies have addressed the non-monotonic relationship between the shallowness of the shells and its critical buckling pressure. However, there is a lack of precise experiments to corroborate these predictions. Using a recently developed technique, we fabricate polymeric spherical shells containing a precise geometric defect. We vary the shallowness of our shells by precisely changing the location of the clamped boundary conditions and measure the critical buckling pressure. Finite element simulations are conducted to analyze the buckling behavior of our shallow shells, in excellent agreement with the experiments. We find that the critical buckling pressure and the shallowness parameter have a decaying sinusoidal relationship, hence, the buckling strength of shallow shells can be larger or smaller than that of complete spherical shells. Moreover, this sinusoidal form is systematically characterized which is affected by a geometric defect. |
Thursday, March 5, 2020 12:51PM - 1:03PM |
S25.00007: Circumferential Buckling of the Confined D-cone Lucia Stein-Montalvo, Kanani Almeida, Douglas Holmes Thin structures deform in dramatic ways to avoid stretching, and this strongly depends on how they are constrained. We observe that in-plane confinement forces the classical packed d-cone to deviate from its characteristic form. Instead of forming a cone with a single region of high stretching, thin, flexible plates wrinkle circumferentially in response to radial and packing-type confinement together. Geometry sets the limiting maximum wavenumber, but dynamic changes in morphology occur even as confinement increases quasi-statically. In a primarily experimental study, we investigate the role of confinement on shape selection, curvature distribution, stretching localization, and the resultant force as waves develop sequentially. |
Thursday, March 5, 2020 1:03PM - 1:15PM |
S25.00008: Investigating imperfection-sensitivity in shell buckling using a toy model Rainer Groh, Alberto Pirrera Shell buckling is known for its extreme sensitivity to initial imperfections. It is generally understood that this sensitivity is caused by an unstable (subcritical) bifurcation, i.e. geometric imperfections rapidly erode the buckling load of the perfect shell. It is less commonly appreciated that subcriticality also creates a strong proclivity for spatially localised buckling modes. The ability of localisations to appear anywhere across the domain (spatial multiplicity) leads to a large set of possible trajectories to instability, with each trajectory affine to a particular imperfection signature. Using a toy model of a link system on a softening elastic foundation, we show that the spatial multiplicity of localisations leads to a large spread in buckling loads, even for indistinguishable random imperfections of the same amplitude. By imposing a dominant imperfection, the strong sensitivity to random imperfections is ameliorated, and the ability to control the trajectory to buckling via dominant imperfections or elastic tailoring, creates interesting possibilities for designing imperfection-insensitive shells. |
Thursday, March 5, 2020 1:15PM - 1:27PM |
S25.00009: Newton’s method for experimental path-following of nonlinear structures Jiajia Shen, Rainer Groh, Robin M Neville, Mark Schenk, Alberto Pirrera Traditional experimental testing of nonlinear structures has not evolved beyond the fundamental techniques of force control (dead loading) and displacement control (rigid loading). These two experimental paradigms face the same issues that computational solvers faced before numerical path-following; namely, limit points in the force-displacement response cannot be traversed by sole force or displacement control. To extend the capabilities of nonlinear testing methods, we have implemented an experimental analogue to numerical path-following. In addition to controlling the displacement at the primary load-introduction points, extra actuators and sensors are attached to control the overall shape of the structure. By perturbing the structure at these control points, and recording the resulting changes in reaction force, an “experimental tangent stiffness” matrix is computed, which is then used in a feedback control system based on Newton’s method. Using an experiment on a shallow arch, we demonstrate the capability of the test setup to path-follow stable and unstable equilibria and traverse limit points. |
Thursday, March 5, 2020 1:27PM - 1:39PM |
S25.00010: Poking imperfect shells to non-destructively predict their buckling loads: success rate and perspectives Emmanuel Virot, Anais Abramian, Emilio Lozano, Tobias Schneider, Shmuel Rubinstein What is the critical load required to crush a soda can or a space rocket shell? |
Thursday, March 5, 2020 1:39PM - 1:51PM |
S25.00011: Canned Wisdom: Probing a Cylindrical Shell’s Memory of Cyclic Loading Nicholas Cuccia, Emmanuel Virot, Michael Phillip Brenner, Shmuel Rubinstein Materials under cyclic loading experience changes in their physical properties, commonly exhibiting structural fatigue, damage and eventually failure. There exists much interest in how a material ‘remembers’ the damage done to it, and few methods exist to, without irreversibly deforming the material, quantitatively describe this ‘memory’. Here, we explore the effects of cyclic loading on the stability of cylindrical shells with many small unknown defects (empty soda-cans). Using a custom-built multi-axial tester, we repeatedly load and unload our cans and generate stability landscapes by measuring the can’s response to non-destructive lateral poking at various axial loads. Here, we will show that cyclic loading changes the can’s reaction to poking, which can be visualized through the evolution of the can’s stability landscape. We will also show how the initial defect structure of our shells can inform their overall fatigue and can be understood via topological features of our shell’s stability landscape. |
Thursday, March 5, 2020 1:51PM - 2:03PM |
S25.00012: Snap-through instability of short and long hyperelastic tubes under inflation Jinwoo Lee, Seonghyeon Kim, Anna Lee We study the bulging behavior of thin cylindrical balloons with various aspect ratios under internal pressure loading. Although the localized bulging of long circular tubes has been extensively studied experimentally and analytically, there is a lack of investigation on the deformation of short and moderate-length tubes. For non-cylindrical balloons, a recent simulation study on the inflation of spheroidal shells reported the boundary aspect ratio that determines the occurrence of localized bulging. We first experimentally investigate the bulging behavior of hyperelastic tubes under internal pressure by systematically varying the aspect ratio. We also explore the effect of prestretch both on the critical bulging pressure and the instability. Then, we compare our experimental results with analytical solutions. Furthermore, we combine multiple tube segments to achieve complex deformation. Our results can be used to understand inflatable biological structures and design soft pneumatic actuators. |
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