Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session P56: Discrete Structures: Geometry, Mechanics, Graphics, and Computation IFocus

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Sponsoring Units: GSNP GSOFT Chair: Pedro Reis, Ecole polytechnique federale de Lausanne Room: BCEC 255 
Wednesday, March 6, 2019 2:30PM  2:42PM 
P56.00001: Exploring the mechanics of curved creased origami with a discrete bar and hinge model Evgueni Filipov, Steven R Woodruff Simulation approaches from computer graphics were some of the first to study the complex geometries and resultant elastic behaviors of curved creased origami. In this work, we present an extension of these approaches by adapting a simplified, discrete, and physicsbased bar and hinge approach to simulate the mechanics of these intriguing origami structures. This model can capture stretching and shearing of the thin sheet, bending of the sheet along principle curvature directions, and bending along the prescribed curved creases. With insight from differential geometry, we use the model to explore the elastic folding sequence, the stiffness, and the global large deformation mechanics of curved crease origami. 
Wednesday, March 6, 2019 2:42PM  2:54PM 
P56.00002: Mapping of Fold Path Bifurcations in Origami Structures Andrew Gillman, Philip Buskohl Origami has proven value in numerous technological applications including lightweight composites, soft robotics, metamaterial design, and deployable space structures, where discrete and modular folding motifs are leveraged to form novel tessellations. The material (stiffness mismatch among deformation modes) and geometric (slender elements) contrasts in origami structures can lead to highly nonlinear mechanical behavior with unique macroscopic properties, such as multistability. To efficiently navigate this complex nonlinear space, we have recently developed an efficient nonlinear truss finite element model with linear eigenanalysis heuristics for branch switching off the flat state. However, more efficient and robust methods have proven essential when performing topology optimization in this nonconvex design space involving energy landscapes with many bifurcations and stable equilibrium points. Our work focuses on the incorporation of robust continuation methods for bifurcation point detection and branch switching to map these multistable energy landscapes and characterize the role of discrete fold stiffness distributions. 
Wednesday, March 6, 2019 2:54PM  3:06PM 
P56.00003: Pairing global symmetries with folding mechanics to transform all periodically triangulated origami D. Zeb Rocklin, James McInerney, Bryan G Chen, Louis Theran, Christian Santangelo Thin sheets restricted to folding at designated creases, as in the traditional Japanese art of origami, have been engineered to deploy devices from the atomic to the macroscopic scale. However, the relation between the crease pattern and the paths to accessible structures is highly nontrivial. We investigate the entire class of periodically triangulated origami, revealing a hidden symmetry between global motions and linear folding mechanisms. Such periodic patterns always admit a twodimensional manifold of cylindrical configurations as previously shown by Tomohiro Tachi. Adding a single quadrilateral face to the unit cell restricts the system to a single degree of freedom without finetuning the geometry. By transforming along these paths, we can change the mechanical response at the boundary. Our analysis can be extended to similar systems with balanced constraints and degrees of freedom such as kirigami, continuum sheets, and magnetic systems. 
Wednesday, March 6, 2019 3:06PM  3:42PM 
P56.00004: MechanicsBased Design for Computational Fabrication Invited Speaker: Emily Whiting Advancements in rapid prototyping technology are closing the gap between what we can simulate with computers and what we can build, as it is now possible to create shapes of astounding complexity. Despite innovations in hardware, however, costly bottlenecks still exist in the design phase. Today’s computational tools for design are largely unaware of the fundamental laws that govern how geometric models will behave in the real world. In this talk I will present recent work combining digital geometry processing, engineering mechanics, and rapid prototyping. The aim is to infuse principles of mechanics into design processes for fabrication. I will highlight specific applications including balance, buoyancy, acoustics, and architectural construction. 
Wednesday, March 6, 2019 3:42PM  3:54PM 
P56.00005: Geodesy: Selfrising 2.5D Tiles by Printing along 2D Geodesic Closed Path Jianzhe Gu, David E. Breen, Jenny Hu, Lifeng Zhu, Ye Tao, Ty Zande, Guanyun Wang, Jessica Yongjie Zhang, Lining Yao Thermoplastic and Fused Deposition Modeling (FDM) based 4D printing is rapidly expanding to allow for space and materialsaving 2D printed sheets morphing into 3D shapes when heated. However, to our knowledge, all the known examples are either origamibased models with obvious folding hinges, or beambased models with holes on the morphing surfaces. Morphing a flat thermoplastic sheet into continuous doublecurvature surfaces remains a challenge, both in terms of a tailored toolpathplanning strategy and a computational model that simulates it. 
Wednesday, March 6, 2019 3:54PM  4:06PM 
P56.00006: Estimating friction in cloth, using simulation and machine learning Abdullah Rasheed, Victor Romero, Florence BertailsDescoubes, Arnaud Lazarus, Stefanie Wuhrer, JeanSebastien Franco We explore the utility of deep neural networks to estimate parameters in cloth motion, specifically the friction coefficient. Our idea is to use realistic cloth motion sequences as video training data for our model and use both spatial and temporal features for parameter estimation. Following recent works, we aim to avoid complex experimental setup for the generation of training data by leveraging cloth simulation as a ground truth model for cloth dynamics. However, this is only meaningful if the simulation is accurate and predictable enough in the range of scenarios envisioned. To ensure realistic simulations, we validate the physical accuracy of Argus, a recent cloth simulator developed in computer graphics which relies on an implicit contact friction solver for capturing exact Coulomb friction. We successfully verify the physical realism of this simulator by conducting physical experiments analogous with simulations, following a protocol previously suggested in literature for measuring Coulomb’s friction coefficient in a Hookean elastic material contacting a rigid surface. We further investigate utilizing a similar protocol for cloth with varying material properties, which is modelled as an orthotropic material in the simulator. 
Wednesday, March 6, 2019 4:06PM  4:18PM 
P56.00007: Discrete Kirchhoff Rod Networks for OptimizationDriven Design Bernhard Thomaszewski, Jonas Zehnder Many examples from architecture, mechanical engineering, and material science can be described as networks of elastic rods. 
Wednesday, March 6, 2019 4:18PM  4:30PM 
P56.00008: Inverse design of a suspended Kirchhoff rod: From theory to practice Victor ROMERO, Florence BertailsDescoubes, Alexandre DerouetJourdan, Arnaud Lazarus Our study focuses on finding the natural shape of a given hanging deformed isotropic rod, made of a known material, the input shape is described as a mere geometric curve that we subsequently frame to compute a material curvature field and feed our inverse problem. 
Wednesday, March 6, 2019 4:30PM  4:42PM 
P56.00009: Jamming limiting the percolation of square tiles on square lattices Eugenio Vogel, Julio F. Valdes, Paulo M. Centres, Antonio J. RamirezPastor Square tiles of k×k sites (k^{2}mers) are deposited irreversibly on L×L square lattices of exactly the same intersite distance; no overlapping is allowed. Coverage is defined as q=Nk^{2}/L^{2}, where N represents the number of deposited tiles. Percolation thresholds q_{p}(k) are reported with high precision for k=1,2, and 3. For k≥4 jamming suppresses percolation. The coverages at which jamming appears q_{j}(k) are also reported accurately [1]. It is observed that q_{p}(2)<q_{j}(2) and q_{p}(3)<q_{j}(3) while this inequality is reversed for k≥4, namely, q_{p}(k)>q_{j}(k), which explains the suppression of percolation for k≥4. Monte Carlo techniques are used to simulate these depositions for k^{2}mers from k=2 to k=100, and lattice sizes with sides much larger than k. Calculations based on exact enumeration were done for k≤6 and several L values to show that this property is inherent to these systems. Finite size scaling is used to estimate the thresholds in the thermodynamic limit. The universality class of this deposition corresponds to random percolation; the corresponding critical exponents nu, gamma, and beta are reported with good accuracy. 
Wednesday, March 6, 2019 4:42PM  4:54PM 
P56.00010: Rotating Matter: The Bearing State Hans Herrmann Granular materials are characterized by an additional degree of freedom, rotations, 
Wednesday, March 6, 2019 4:54PM  5:06PM 
P56.00011: Nonequilibrium dynamics of isostatic spring networks Federico Gnesotto, Benedikt Remlein, Chase Broedersz Mechanical systems exhibit rich critical behavior in the vicinity of the isostatic point. Inspired by living matter such as cytoskeletal networks and tissue, we here consider marginal assemblies driven out of equilibrium by internal activity. To date it remains unclear how the critical nature of such systems affects their nonequilibrium dynamics. We elucidate the role of the isostatic threshold in active diluted spring networks: heterogeneously distributed active noise sources drive the system into a nonequilibrium steady state. The nonequilibrium dynamics between pairs of network nodes are quantified by the characteristic cycling frequency ω—a measure of the circulation of the associated phase space currents. We reveal critical scaling of the cycling frequencies and intuitively understand their local behavior employing a meanfield approach. Overall, our work serves as a bridge connecting the wellestablished theory of mechanical stability to the novel field of nonequilibrium statistical mechanics. 
Wednesday, March 6, 2019 5:06PM  5:18PM 
P56.00012: The Duality of Networks in Jammed Granular Packings Deshpreet Bedi, Bulbul Chakraborty Contact networks in jammed granular systems, derived from contact forces between dry grains in mechanical equilibrium, can be represented in a dual force space as a network of edges that form a spacefilling tiling. This force tiling paradigm has been found to be particularly useful in the characterization of stressinduced transitions in granular materials. As a generic network itself, the force network can be studied with techniques used in the investigation of more conventional networks. 
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