Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session S06: Soft Mechanics via Geometry IFocus Live
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Sponsoring Units: DSOFT DPOLY Chair: Moumita Das, Rochester Institute of Technology Room: 06 |
Thursday, March 18, 2021 11:30AM - 11:42AM Live |
S06.00001: Interacting dislocations create shape multistability in flexible cylindrical crystals Andrei Zakharov, Daniel A Beller Many biological and synthetic systems are self-organized in the form of ordered two-dimensional assemblies, including microtubules, carbon nanotubes and colloidal systems. Motivated by these observations and topological defects associated with geometrically frustrated tubular assemblies, we investigate a minimal model of dislocation dynamics in flexible 2D crystals wrapped into a cylindrical topology. We theoretically study how interacting dislocations distort the crystalline order and affect the three-dimensional shape - bends, kinks, and helicity - of tubular crystals. Using numerical simulations we explore plastic deformations by dislocation glide. We demonstrate that the periodicity of cylindrical topology leads to states where glide is energetically restricted, allowing precise prediction of defect location, and creating multiple metastable tube geometries that do not exist in crystals on rigid cylindrical surfaces. We also show that transitions between metastable defect patterns associated with different 3D shapes can be triggered by applied external stress. This opens possibilities for designing mechanically multistable systems of target geometry, topology and shape. |
Thursday, March 18, 2021 11:42AM - 11:54AM Live |
S06.00002: A fragmentation-based model for the crumpling of thin sheets Jovana Andrejevic, Lisa M Lee, Shmuel M Rubinstein, Christopher Rycroft Crumpled systems are prime examples of complexity and disorder: As a thin sheet is confined, an intricate network of creases emerges spontaneously in regions of high localized stress. However, these systems can exhibit unexpected order: For example, the total length of creases which form in repeatedly crumpled Mylar sheets was found to grow logarithmically in the number of crumpling cycles. We propose a physical explanation for this behavior by considering crumpling as a fragmentation process, partitioning a sheet into facets whose area distribution evolves according to a kinetic equation for fragmentation. We develop a model for how the facet area distribution changes incrementally over one crumpling cycle based on geometric frustration between existing facets and the confining container. Our model captures the gradual compliance of the sheet which slows damage accumulation in agreement with the observed logarithmic scaling. We conclude by investigating these observations in a computational model of thin elastoplastic sheets, which enables deeper exploration of complex phenomena such as spatial damage evolution. |
Thursday, March 18, 2021 11:54AM - 12:06PM Live |
S06.00003: A computational model of thin sheets crumpled via twisting Madelyn Leembruggen, Jovana Andrejevic, Arshad Kudrolli, Christopher Rycroft Crumpling occurs across all length scales, sometimes arising as a feature (such as the energy-dissipating crushing of a car body during a collision) and other times as a bug (like material damage or failure in industrial manufacturing processes). In all instances, it is essential we understand the complex buckling and wrinkling modes which result in disordered, crumpled configurations. These mechanical transitions remain poorly understood, although some progress has come through studying the crease networks of physically crumpled thin sheets. To supplement these experimental snapshots, we introduce an efficient computational model for thin sheets that reproduces their mechanical properties and captures the phenomenology of plastic deformation under confinement. Our simulations allow careful analysis of the sheet’s topography and curvature; temporal resolution of damage accumulation and ridge fragmentation; and reveal the hidden internal energy dynamics of the intricate, evolving system. |
Thursday, March 18, 2021 12:06PM - 12:18PM Live |
S06.00004: Boundary Effects on Thin Film Wrinkling Patterns Lauren Dutcher, Carmen Lee, Kari Dalnoki-Veress Wrinkle formation is a phenomenon seen universally in nature and can be examined using a simple bilayer thin film geometry. In our work, wrinkling is initiated by a thermally induced compressive stress in a rigid capping film placed atop a thin liquid film. The thickness of both films affect the wrinkling wavelength, amplitude and shape. Previous experiments have characterized the wrinkling wavelength and amplitude, but the wrinkling patterning has garnered less attention. We focus on the effect of boundaries on the wrinkling patterns. Of specific interest is the effect of a step in the liquid film thickness on the wrinkling morphologies. Since a variation in the thickness of the underlying liquid film affects the wavelength and amplitude of the capping film, the stepped liquid film causes a mismatch in the wavelength at the boundary. Optical and atomic force microscopy are used to analyze two sample geometries: linear and circular stepped boundary conditions. |
Thursday, March 18, 2021 12:18PM - 12:30PM Live |
S06.00005: Non-Hookean Elasticity of 2D Model Tissue Arthur Hernandez, M Cristina Marchetti, Mark J Bowick, Michael Moshe, Michael F Staddon We study the peculiar mechanical response of a mean-field approximation to the vertex model (VM) of 2D epithelia. In the absence of T1 rearrangements, the VM exhibits a transition between a soft and a stiff solid tuned by the target shape index of the cells and is associated with the onset of geometric incompatibility. By examining the response to a variety of deformations, we show that the stiff-solid phase exhibits nonlinear elastic response that cannot be recast in the framework of conventional Hookean elasticity, even in the limit of infinitesimal strain. Instead, the linear mechanical response, when allowing shape change, depends on the specific protocol used for the imposed deformation and is not therefore fully characterized by two independent elastic moduli, as in the linear elasticity of a 2D isotropic solid. Our numerical simulations lend support to these conclusions. |
Thursday, March 18, 2021 12:30PM - 12:42PM Live |
S06.00006: Criticality in subisostatic spring networks stabilized by thermal fluctuations Sadjad Arzash, Anupama Gannavarapu, Amanda Marciel, Frederick MacKintosh A variety of elastic structures can be modeled by interconnected networks of Hookean springs. As Maxwell showed, such spring networks with connectivity below a critical or isostatic threshold are unstable for small deformations. These subisostatic networks, however, can be stabilized by various mechanisms including adding interactions such as bending rigidity between adjacent bonds or springs. It is also possible to stabilize otherwise floppy spring networks by thermal fluctuations. Under nonlinear deformations, however, even subisostatic spring networks undergo a phase transition from a floppy to a rigid state. This transition is critical in nature and exhibits a variety of critical exponents near a critical strain that depends on network connectivity. Here, we explore the criticality aspects of this strain-induced transition in presence of thermal fluctuations. |
Thursday, March 18, 2021 12:42PM - 12:54PM Live |
S06.00007: "Wrinkling in growing hyperelastic annular plates" SUMIT MEHTA, Gangadharan Raju, Prashant Saxena In this work, we have investigated the mechanical instability in an isotropic hyperelastic growing annular plate subjected to traction on the inner and the outer edge. A three-dimensional system under finite strain with general traction condition is formulated using a variational approach for an incompressible annular plate. The system is reduced to a two-dimensional plate system using series expansion in terms of thickness variable and corresponding governing equations are obtained. These equations are solved for axisymmetric deformations and growth conditions - both radial and circumferential direction in the incompressible hyperelastic material. The aim of this work is to demonstrate the effect of growth and loading conditions on the wrinkling behavior of annular plates subjected to large deformation during contraction. The stability analysis is performed by perturbing the homogeneous system with small parameters and analyze the onset of instability in a growing region. The results obtained are applicable to skin wrinkling during wound healing and buckling patterns induced during swelling of gels. |
Thursday, March 18, 2021 12:54PM - 1:06PM Live |
S06.00008: Mechanical Adaptability of Patterns in Confined Hydrogels Yao Xiong, Olga Kuksenok Pattern formation and dynamic restructuring plays a critical role in a plethora of natural processes. Controlling pattern formation dynamically in soft synthetic materials would allow one to control an entire range of surface functionalities. Herein, we focus on the dynamic restructuring between different patterns in thermoresponsive poly(N-isopropylacrylamide) membranes constrained between two rigid surfaces. We use three-dimensional gel Lattice Spring Model to simulate the dynamics of constrained hydrogels. Mechanical instability due to the constrained swelling of a polymer network undergoing extensive volume changes in response to external stimuli results in pattern formation in these systems. We show that the wavelength, the amplitude, and the mode of patterns formed could be controlled dynamically by varying the rates of stretching and compression the sample along its width. Furthermore, the sample exhibits bistability, which in turn is controlled by the rates of the stretching and compression. In effect, our results indicate that the sample has an effective memory of previous state. Our results point out that the functionality of soft structured interfaces can be controlled dynamically via mechanical forcing. |
Thursday, March 18, 2021 1:06PM - 1:18PM Live |
S06.00009: Snap-shaping groovy sheets Anne Meeussen, Martin Van Hecke Shape-morphing structures are useful for a host of real-life applications- but a general design strategy is lacking. We showcase controlled, reversible and fast shape-morphing in macroscopic corrugated sheets. Snap-through events in the sheet's corrugations form stable scar lines that locally stretch the sheet. Competition between bending and stretching gives rise to a host of passively stable, 3-D shapes, which can be described as a sub-class of ruled surfaces. Our work provides a platform where passive multistability produces controlled shape-morphing. |
Thursday, March 18, 2021 1:18PM - 1:54PM Live |
S06.00010: Decoding mechanics by just looking (and not deforming) Invited Speaker: J. M. Schwarz How does one determine whether or not a frictional particle packing or biological cells tiling a surface is a rigid material? To answer this question, one typically deforms the material. Rigid materials resist deformations, while floppy ones do not. And yet, constraint-counting methods, relying solely on contact network topology, can identify rigid structures within a frictional particle packing. Additionally, the geometry of cell shapes can help determine whether or not a confluent biological tissue is rigid. Newer examples of “looking but not deforming” mechanics will be discussed, such as area-conserving loops embedded within a fiber network to drive nonlinear compression mechanics as well as convexity-driven rigidity transitions more generally, with an eye towards illuminating the universal design principles for materials that can readily toggle between ultra-responsive and ultra-robust mechanics. |
Thursday, March 18, 2021 1:54PM - 2:06PM Not Participating |
S06.00011: Geometric mechanics of thin sheets with cuts and folds Lauren Niu, Gaurav Chaudhary, L. Mahadevan The presence of cuts and creases in thin planar sheets can dramatically alter their mechanical and geometrical response to loading. To quantify this, we perform numerical experiments to characterize the geometric mechanics of sheets as a function of the number, size and orientation of cuts and creases. We show that the mechanical behavior of these sheets with one or a few cuts or creases can be understood in terms of simple scaling-laws, while the geometry of the deformed sheets can be approximated via a composition of simple developable units - flats, cylinders and cones - in the small and large deformation limit. We conclude by generalizing the results to characterize the geometric mechanics of sheets with more complex distributions of cuts and creases. |
Thursday, March 18, 2021 2:06PM - 2:18PM Live |
S06.00012: Statistical Mechanics of Low Angle Grain Boundaries in Two Dimensions Grace H. Zhang, David Robert Nelson We explore order in low angle grain boundaries (LAGBs) embedded in a two-dimensional crystal at thermal equilibrium. Symmetric LAGBs subject to a periodic Peierls potential undergo, with increasing temperatures, a thermal depinning transition, above which the potential is irrelevant at long wavelengths and the LAGB exhibits transverse fluctuations that grow logarithmically with inter-dislocation distance. Longitudinal fluctuations lead to a series of melting transitions marked by the sequential disappearance of diverging algebraic Bragg peaks with universal critical exponents. Aspects of our theory are checked by a mapping onto random matrix theory. |
Thursday, March 18, 2021 2:18PM - 2:30PM Live |
S06.00013: Discrete Symmetries Govern Folding of Quadrilateral-based Origami James McInerney, Glaucio Paulino, Zeb Rocklin The past decade has seen origami’s rise as a candidate for elastic metamaterials granting properties such as negative Poisson ratios. While we have recently shown a pairing between rigid body modes and folding motions in periodic triangulations, many applications utilize quadrilateral faces to control the mechanical response, requiring engineered symmetries such as the parallelogram faces used in crease patterns like the Miura-ori, eggbox, Barreto’s Mars, and block fold. Here we present a novel formalism that reduces the conventional 3-vector constraints at each vertex to scalar constraints on each edge that describe the infinitesimal deformations, including face bending, of generic quadrilateral-based patterns. These modes are governed by a constraint matrix — resembling a quantum Hamiltonian — that can be decomposed into disjoint sectors of solutions in the presence of discrete symmetries. We place special emphasis on a class of parallelogram origami, including all of the aforementioned crease patterns, exhibiting a permutation symmetry for which we obtain analytical expressions for their linear deformations, revealing such crease patterns always exhibit a single auxetic mode. |
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