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 V06: Soft Mechanics via Geometry IIFocus Live

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Sponsoring Units: DSOFT DPOLY Chair: Zeb Rocklin, Georgia Institute of Technology Room: 06 
Thursday, March 18, 2021 3:00PM  3:12PM Live 
V06.00001: Geometric approach to Mechanical design principles in continuous elastic sheet Michal Arieli, Sharon Eran, Michael Moshe We present a systematic theoretical method for controlling and manipulating mechanical properties of slender solids. Using a geometric approach to nonEuclidean elasticity we show that the energy landscape in configuration space can be sculpted and manipulated by controlling material geometric properties such as preferred rest lengths and curvatures. We mathematically formalize an inverse design problem, and show that by implanting geometric frustration, extreme mechanical properties can be encoded into a materials using accessible experimental techniques. To test the methodology we focus on a family of structures that present anomalous mechanical behavior such as tunable and even vanishing rigidity. The presented formalism can be discretized and thus opens a new pathway for the design of both continuum and discrete solids and structures. 
Thursday, March 18, 2021 3:12PM  3:24PM Live 
V06.00002: Fracture behavior of 2D Disordered Network Mechanical Metamaterials Marcos ReyesMartinez, Edwin Chan, Christopher Soles, Kieran A Murphy, Daniel Reid, Heinrich Jaeger, Sidney Robert Nagel, Juan De Pablo Disordered network mechanical metamaterials (DNMM), comprised of random arrangements of bonds and nodes, have emerged from theoretical and experimental studies as promising candidates for metamaterials with highly tunable elastic constants. This tunability is achieved through a computational approach called pruning that systematically removes bonds while optimizing for either the bulk or shear modulus. We take advantage of the pruning approach to study fracture behavior in 2D DNMMs. We perform quasistatic tensile testing to study the role of network architecture in controlling crack propagation. Unpruned and pruned networks with systematically varying bond thickness and materials (Silicone elastomer, Nylon 6 and Acrylic) are studied. We elucidate the impact of network architecture in strain localization during crack propagation and how it relates to the overall toughness of the networks. Our experiments demonstrate that it is crucial to finely control the bulk to shear modulus ratio of the DNMM to control toughness. This ratio describes the ability to change shape over its ability to change volume. The principles learned from the study of DNMMs with finely tuned local elastic properties might provide an effective route for materials with improved tearresistant properties. 
Thursday, March 18, 2021 3:24PM  3:36PM Live 
V06.00003: Characteristics of transition to disclination disorder on curved crystalline surfaces Siddhansh Agarwal, Sascha Hilgenfeldt In many engineering or biological contexts, twodimensional lattices structures have to reconcile regular crystalline order with intrinsic curvature, such as the periodic tiling of ommatidia in bulging anthropod eyes or the selfassembly of protein monomers to form viral capsids. We previously described a criterion derived directly from shape properties of the surface that is an accurate predictor of whether a curved structure can be defectfree or not. In practice, however, this transition is modified by activation barriers or more favorable intermediate positions. The shape of the energy landscape determines if a transition preserves the symmetry of defect placement because an energy barrier must be overcome or breaks the symmetry due to stable intermediate positions. While backed by numerical computations, we derive and understand these findings analytically, demonstrating that the dependence of transition characteristics can be predicted a priori for general surface shapes. These results give practical insight into transitions to disorder in many ordered biological systems and inform material design considerations through geometric control, while also improving our fundamental understanding. 
Thursday, March 18, 2021 3:36PM  3:48PM Live 
V06.00004: Convexity induced rigidity transitions Mahesh Gandikota, Amanda Parker, J M Schwarz A fundamental theorem in rigidity theory due to Cauchy states that all convex polyhedrons in three dimensions are rigid, i.e. the polyhedron cannot be deformed without changing the shape of at least one of its faces at some energy cost. However, a polygon in two dimensions is floppy irrespective of its convexity and can be deformed with no energy cost. This property is consistent with Maxwell's constraint counting scheme. Our numerical results show that under finite isotropic expansion, an areaconserving polygon rigidifies when it achieves convexity, as does two areaconserving polygons sharing an edge. This demonstrates a link between geometry and mechanics. We finally study 2D spring networks with several edge sharing polygons. We determine the existence of a rigidityconvexity correspondence in the spring network under isotropic expansion. 
Thursday, March 18, 2021 3:48PM  4:00PM Live 
V06.00005: Isigami: a Novel Highly Reconfigurable Surface Benjamin Katz, Vincent Henry Crespi

Thursday, March 18, 2021 4:00PM  4:12PM Live 
V06.00006: The effect of boundary curvature on the wrinkling of thin suspended films Stoffel Janssens, Burhannudin Sutisna, Alessandro Giussani, David Vazquez Cortes, Eliot Fried Wrinkling is a ubiquitous phenomenon in nature that can be used to optimize the performance of devices [1]. However, few basic tools are available to predict the wrinkling of thin films due to the intricate mechanics that are involved [2]. Here, we show a relation between the boundary curvature κ and the wrinkle wavelength λ of a thin suspended film under boundary confinement [3]. Experiments are done with nanocrystalline diamond films of approximate thickness 184 nm that are grown on glass substrates. By etching parts of substrate after growth, suspended films with circular boundaries of radius ranging from 30 to 811 μm are made using recent technologies [4,5]. Due to thermal mismatch, the parts of film attached to the substrate are compressively strained and the suspended parts of film are azimuthally wrinkled. We show that λ monotonically decreases with κ and present a model that predicts this. 
Thursday, March 18, 2021 4:12PM  4:48PM Live 
V06.00007: Shapes on a plane: mechanical properties of geometric models of tissue Invited Speaker: Daniel Sussman What governs the motion of cells inside an organism, or the collective mechanical properties of cells composing a tissue? The mechanical and dynamical properties of dense biological matter – e.g., whether it can support stresses, or whether it has surface tension – are obviously important for its biological function, but how can we coarse grain from the properties of single cells to try to understand the rich variety of collective behavior seen in these “living materials?” In this talk, I will discuss a theoretical framework for understanding dense cellular matter that coarse grains complex biological units into entirely geometric entities. I will also discuss how this family of geometrical models are different from alternative coarsegraining apporaches, focusing on the unusual structure of these models and the unique predictions they make for the behavior of real dense biological tissues. 
Thursday, March 18, 2021 4:48PM  5:00PM Live 
V06.00008: Thermal fluctuations of singular mechanical networks Manu Mannattil, J. M. Schwarz, Christian Santangelo Mechanical networks, like many constrained systems, are often characterized by singularities in their configuration manifolds due to states of self stress—equilibrium states with nonzero internal forces allowed by the geometry of the network. Examples of such systems include linkages and origami, which are typically modeled as ballandspring networks that often support selfstress states. In this study, we explore the geometric and topological origins of these singularities and their effects when such networks are equilibrated with a thermal bath. Self stresses can also give rise to additional infinitesimal zero modes, which are perturbations that preserve the constraints to linear order. Working with stiff networks at low temperatures, we use analytical calculations and simulations to find the existence of a nontrivial coupling between infinitesimal zero modes, harmonic modes, and coordinates on the configuration manifold. This coupling manifests itself as an enhancement of equilibrium probability density near these singularities. This, in turn, has a direct effect on measurable thermodynamic observables, which display atypical thermal scaling. 
Thursday, March 18, 2021 5:00PM  5:12PM Live 
V06.00009: Perfectly Imperfect Origami: How the imperfections in selffolding origami allow robust folding Mary Elizabeth LeeTrimble, JiHwan Kang, Ryan Hayward, Christian Santangelo Selffolding origami are engineered flat sheets that can fold into three dimensional structures when external stimuli are applied. In application, these structures are vulnerable to misfolding. To attempt to understand this misfolding problem, we introduce a bar and hinge model for selffolding, triangulated origami that allows both face stretching and face bending. Using this model, we use a single vertex fourfold origami called the birdsfoot to probe how the addition of these imperfections influence when the birdsfoot is bistable for given sets of programmed equilibrium angles. In both our theoretical predictions and a set of experiments where two of the birdsfoot’s faces are intentionally weakened, we see two competing effects. More face stretching leads to fewer sets of programmed angles in which the birdsfoot is bistable, while weakening faces leads to more bistable sets of programmed angles. We then turn to the Randlett bird, a more complex origami, and simulate its misfolding rates with different allowed amounts of face stretching and bending, and again see an interplay between the two effects. Collectively, these results seem to indicate that it is actually the imperfections in our experimental systems that allow robust folding. 
Thursday, March 18, 2021 5:12PM  5:24PM Live 
V06.00010: Statistical mechanics of 2D sheets under uniaxial tension Mohamed El Hedi Bahri, Siddhartha Sarkar, Andrej Kosmrlj Atomically thin sheets, such as graphene, are widely used in nanotechnology. Recently they have also been used in applications including kirigami and selffolding origami, where it becomes important to understand how they respond to external loads. Motivated by this, we investigate how isotropic sheets respond to uniaxial tension by employing the renormalization group. Previously, it was shown that for freely suspended sheets thermal fluctuations effectively renormalize elastic constants, which become scaledependent beyond a characteristic thermal length scale (a few nanometers for graphene at room temperature), beyond which the bending rigidity increases, while the inplane elastic constants reduce with universal power law exponents. For sheets under uniaxial tension, we find that beyond a stressdependent length scale the Young’s modulus in the orthogonal direction scales with a different exponent. In addition, for moderate tensions we find a universal nonlinear forcedisplacement relation. For large tensions, inplane fluctuations longitudinal with the axis of tension are suppressed and classical mechanics along this axis is recovered. 
Thursday, March 18, 2021 5:24PM  5:36PM Live 
V06.00011: Spontaneous Tilt of Thermalized Elastic Sheets Zhitao Chen, Duanduan Wan, Mark J Bowick Through molecular dynamic simulations and theoretical analysis, we show that a thermalized elastic sheet clamped on one edge spontaneously tilts out of the plane of clamping, hence breaking the inversion symmetry of the system. For a given temperature, a rectangular sheet only tilts if its aspect ratio is sufficiently large. Using the thermalized membrane as a reference state, we show that tilt is a type of buckling instability. We derive the critical aspect ratio for tilt as a function of temperature by analyzing the inplane stress and strain of the elastic sheet due to clamping. 
Thursday, March 18, 2021 5:36PM  5:48PM Live 
V06.00012: Changing the jamming transition with auxetic metagrains Daan Haver, Corentin Coulais The collective behaviour of granular material has been a topic of intense research to accurately describe natural phenomena such as the liquidlike behaviour found in avalanches and hourglasses to the solidlike behaviour experienced when walking across the beach. The transition from liquidlike to solidlike behaviour can be ascribed to a critical packing fraction. Here, we study how this transition can be tweaked by introducing a fourbarlinkage in all grains in the packing. This metagranular packing can therefore adapt to a high external pressure by selfadjusting the packing fraction. We show that, upon shearing, the auxetic property facilitates yielding of individual grains. As a direct result, the dilatancy effect observed in the packing is also much less significant. This work provides a novel method to selfadjust a close packing into the shearjammed regime, preventing jamming inside the packing. 
Thursday, March 18, 2021 5:48PM  6:00PM Live 
V06.00013: Statistical mechanics of nanotubes Siddhartha Sarkar, Mohamed El Hedi Bahri, Andrej Kosmrlj We investigate the effect of thermal fluctuations on the mechanical properties of nanotubes by employing tools from statistical physics. For 2D sheets it was previously shown that thermal fluctuations effectively renormalize elastic constants beyond a characteristic temperaturedependent thermal length scale (a few nanometers for graphene at room temperature), where the bending rigidity increases, while the inplane elastic constants reduce in a scaledependent fashion with universal power law exponents. However, the curvature of nanotubes produces new phenomena. In nanotubes, competition between stretching and bending costs associated with radial fluctuations introduces a characteristic elastic length scale, which is proportional to the geometric mean of the radius and effective thickness. Beyond elastic length scale, we find that the inplane elastic constants stop renormalizing in the axial direction, while they continue to renormalize in the circumferential direction beyond the elastic length scale albeit with different universal exponents. The bending rigidity, however, stops renormalizing in the circumferential direction at the elastic length scale. These results were verified using molecular dynamics simulations. 
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