1
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Flaum E, Prakash M. Curved crease origami and topological singularities enable hyperextensibility of L. olor. Science 2024; 384:eadk5511. [PMID: 38843314 DOI: 10.1126/science.adk5511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Accepted: 04/12/2024] [Indexed: 06/15/2024]
Abstract
Fundamental limits of cellular deformations, such as hyperextension of a living cell, remain poorly understood. Here, we describe how the single-celled protist Lacrymaria olor, a 40-micrometer cell, is capable of reversibly and repeatably extending its necklike protrusion up to 1200 micrometers in 30 seconds. We discovered a layered cortical cytoskeleton and membrane architecture that enables hyperextensions through the folding and unfolding of cellular-scale origami. Physical models of this curved crease origami display topological singularities, including traveling developable cones and cytoskeletal twisted domain walls, which provide geometric control of hyperextension. Our work unravels how cell geometry encodes behavior in single cells and provides inspiration for geometric control in microrobotics and deployable architectures.
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Affiliation(s)
- Eliott Flaum
- Graduate Program in Biophysics, Stanford University, Stanford, CA, USA
- Department of Bioengineering, Stanford University, Stanford, CA, USA
| | - Manu Prakash
- Graduate Program in Biophysics, Stanford University, Stanford, CA, USA
- Department of Bioengineering, Stanford University, Stanford, CA, USA
- Department of Biology (courtesy), Stanford University, Stanford, CA, USA
- Department of Oceans (courtesy), Stanford University, Stanford, CA, USA
- Woods Institute for the Environment, Stanford University, Stanford, CA, USA
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2
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Dai CF, Zhu QL, Khoruzhenko O, Thelen M, Bai H, Breu J, Du M, Zheng Q, Wu ZL. Reversible Snapping of Constrained Anisotropic Hydrogels Upon Light Stimulations. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2024:e2402824. [PMID: 38704682 DOI: 10.1002/advs.202402824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Revised: 04/12/2024] [Indexed: 05/07/2024]
Abstract
Creatures, such as Venus flytrap and hummingbirds, capable of rapid predation through snap-through transition, provide paradigms for the design of soft actuators and robots with fast actions. However, these artificial "snappers" usually need contact stimulations to trigger the flipping. Reported here is a constrained anisotropic poly(N-isopropylacrylamide) hydrogel showing fast snapping upon light stimulation. This hydrogel is prepared by flow-induced orientation of nanosheets (NSs) within a rectangular tube. The precursor containing gold nanoparticles is immediately exposed to UV light for photopolymerization to fix the ordered structure of NSs. Two ends of the slender gel are clamped to form a buckle with bistability nature, which snaps to the other side upon laser irradiation. Systematic experiments are conducted to investigate the influences of power intensity and irradiation angle of the laser, as well as thickness and buckle height of the gel, on the snapping behaviors. The fast snapping is further used to kick a plastic bead and control the switch state. Furthermore, synergetic or oscillated snapping of the gel with two buckles of opposite directions is realized by inclined irradiation of a laser or horizontal irradiation with two lasers, respectively. Such light-steered snapping of hydrogels should merit designing soft robots, energy harvests, etc.
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Affiliation(s)
- Chen Fei Dai
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310058, China
| | - Qing Li Zhu
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310058, China
| | - Olena Khoruzhenko
- Bavarian Polymer Institute and Department of Chemistry, University of Bayreuth, Universitätsstrasse 30, 95440, Bayreuth, Germany
| | - Michael Thelen
- Bavarian Polymer Institute and Department of Chemistry, University of Bayreuth, Universitätsstrasse 30, 95440, Bayreuth, Germany
| | - Huiying Bai
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310058, China
| | - Josef Breu
- Bavarian Polymer Institute and Department of Chemistry, University of Bayreuth, Universitätsstrasse 30, 95440, Bayreuth, Germany
| | - Miao Du
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310058, China
| | - Qiang Zheng
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310058, China
| | - Zi Liang Wu
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310058, China
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3
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Li CY, Zheng SY, Hao XP, Hong W, Zheng Q, Wu ZL. Spontaneous and rapid electro-actuated snapping of constrained polyelectrolyte hydrogels. SCIENCE ADVANCES 2022; 8:eabm9608. [PMID: 35417235 PMCID: PMC9007498 DOI: 10.1126/sciadv.abm9608] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 02/24/2022] [Indexed: 05/23/2023]
Abstract
Venus flytrap and bladderwort, capable of rapid predation through a snapping transition, have inspired various designs of soft actuators and robots with fast actions. These designs, in contrast to their natural counterparts, often require a direct force or pressurization. Here, we report a bistable domal hydrogel structure capable of spontaneous and reversible snapping under an electric field. Unlike a mechanical force, the electric field does not drive the gel directly. Instead, it redistributes mobile ions that direct the migration of water molecules and bends the polyelectrolyte hydrogel. Subject to constraint from surrounding neutral gel, the elastic energy accumulates until suddenly released by snapping, just like the process in natural organisms. Several proof-of-concept examples, including an optical switch, a speedy catcher, and a pulse pump, are designed to demonstrate the versatile functionalities of this unit capable of articulate motion. This work should bring opportunities to devise soft robotics, biomedical devices, etc.
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Affiliation(s)
- Chen Yu Li
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Si Yu Zheng
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Xing Peng Hao
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Wei Hong
- Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Qiang Zheng
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Zi Liang Wu
- Ministry of Education Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, China
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4
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Fernandes Minori A, Jadhav S, Chen H, Fong S, Tolley MT. Power Amplification for Jumping Soft Robots Actuated by Artificial Muscles. Front Robot AI 2022; 9:844282. [PMID: 35308461 PMCID: PMC8927657 DOI: 10.3389/frobt.2022.844282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2021] [Accepted: 02/01/2022] [Indexed: 12/04/2022] Open
Abstract
Robots composed of soft materials can passively adapt to constrained environments and mitigate damage due to impact. Given these features, jumping has been explored as a mode of locomotion for soft robots. However, for mesoscale jumping robots, lightweight and compact actuation are required. Previous work focused on systems powered by fluids, combustion, smart materials, electromagnetic, or electrostatic motors, which require one or more of the following: large rigid components, external power supplies, components of specific, pre-defined sizes, or fast actuation. In this work, we propose an approach to design and fabricate an electrically powered soft amplification mechanism to enable untethered mesoscale systems with continuously tunable performance. We used the tunable geometry of a liquid crystal elastomer actuator, an elastic hemispherical shell, and a pouch motor for active latching to achieve rapid motions for jumping despite the slow contraction rate of the actuator. Our system amplified the power output of the LCE actuator by a factor of 8.12 × 103 with a specific power of 26.4 W/kg and jumped to a height of 55.6 mm (with a 20 g payload). This work enables future explorations for electrically untethered soft systems capable of rapid motions (e.g., jumping).
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Affiliation(s)
- Adriane Fernandes Minori
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, United States
- School of Computer Science, Human and Computer Interaction Institute, Carnegie Mellon University, Pittsburgh, PA, United States
| | - Saurabh Jadhav
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, United States
| | - Haojin Chen
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, United States
| | - Samantha Fong
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, United States
| | - Michael T. Tolley
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, United States
- *Correspondence: Michael T. Tolley,
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5
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Fraldi M, Palumbo S, Cutolo A, Carotenuto AR, Guarracino F. On the equilibrium bifurcation of axially deformable holonomic systems: solution of a long-standing enigma. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0327] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The stability of equilibrium is a fundamental topic in mechanics and applied sciences. Apart from its central role in most engineering fields, it also arises in many natural systems at any scale, from folding/unfolding processes of macromolecules and growth-induced wrinkling in biological tissues to meteorology and celestial mechanics. As such, a few key models represent essential benchmarks in order to gain significant insights into more complex physical phenomena. Among these models, a cornerstone is represented by a structure made of two straight axially deformable bars, connected by an elastic hinge and simply supported at the ends, which are capable of buckling under a compressive axial force. This classical example has been proposed and analysed in some depth by Feodosyev but the attention is here focused on an apparently paradoxical result given by this model, i.e. the existence of a lower bound for the axial-to-flexural stiffness ratio in order for the bifurcation to take place. This enigma is solved theoretically by showing that, differently from other classical stability problems, constitutive and geometric nonlinearities cannot be
a priori
disconnected and an ideal linearized axial constitutive law cannot be employed in this case. The theory is validated with an experiment, and post-buckling and energy extrema of the proposed solution are discussed as well, highlighting possible snap-back and snap-through phenomena. Finally, the results are extended to the complementary case of tensile buckling.
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Affiliation(s)
- M. Fraldi
- Department of Structures for Engineering and Architecture, University of Napoli ‘Federico II’, Napoli, Italy
- Interdisciplinary Research Center of Structural Composites for Innovative Constructions, University of Napoli ‘Federico II’, Napoli, Italy
| | - S. Palumbo
- Department of Structures for Engineering and Architecture, University of Napoli ‘Federico II’, Napoli, Italy
| | - A. Cutolo
- Department of Structures for Engineering and Architecture, University of Napoli ‘Federico II’, Napoli, Italy
| | - A. R. Carotenuto
- Department of Structures for Engineering and Architecture, University of Napoli ‘Federico II’, Napoli, Italy
| | - F. Guarracino
- Department of Structures for Engineering and Architecture, University of Napoli ‘Federico II’, Napoli, Italy
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6
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Kernes J, Levine AJ. Geometrically induced localization of flexural waves on thin warped physical membranes. Phys Rev E 2021; 103:053002. [PMID: 34134269 DOI: 10.1103/physreve.103.053002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2020] [Accepted: 04/28/2021] [Indexed: 11/07/2022]
Abstract
We consider the propagation of flexural waves across a nearly flat, thin membrane, whose stress-free state is curved. The stress-free configuration is specified by a quenched height field, whose Fourier components are drawn from a Gaussian distribution with power-law variance. Gaussian curvature couples the in-plane stretching to out-of-plane bending. Integrating out the faster stretching modes yields a wave equation for undulations in the presence of an effective random potential, determined purely by geometry. We show that at long times and lengths, the undulation intensity obeys a diffusion equation. The diffusion coefficient is found to be frequency dependent and sensitive to the quenched height field distribution. Finally, we consider the effect of coherent backscattering corrections, yielding a weak localization correction that decreases the diffusion coefficient proportional to the logarithm of the system size, and induces a localization transition at large amplitude of the quenched height field. The localization transition is confirmed via a self-consistent extension to the strong disorder regime.
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Affiliation(s)
- Jonathan Kernes
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA
| | - Alex J Levine
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA.,Department of Chemistry and Biochemistry, UCLA, Los Angeles California 90095-1596, USA.,Department of Computational Medicine, UCLA, Los Angeles, California 90095-1596, USA
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7
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Oshri O. Volume-constrained deformation of a thin sheet as a route to harvest elastic energy. Phys Rev E 2021; 103:033001. [PMID: 33862743 DOI: 10.1103/physreve.103.033001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2020] [Accepted: 02/08/2021] [Indexed: 11/07/2022]
Abstract
Thin sheets exhibit rich morphological structures when subjected to external constraints. These structures store elastic energy that can be released on demand when one of the constraints is suddenly removed. Therefore, when adequately controlled, shape changes in thin bodies can be utilized to harvest elastic energy. In this paper, we propose a mechanical setup that converts the deformation of the thin body into a hydrodynamic pressure that potentially can induce a flow. We consider a closed chamber that is filled with an incompressible fluid and is partitioned symmetrically by a long and thin sheet. Then, we allow the fluid to exchange freely between the two parts of the chamber, such that its total volume is conserved. We characterize the slow, quasistatic, evolution of the sheet under this exchange of fluid, and derive an analytical model that predicts the subsequent pressure drop in the chamber. We show that this evolution is governed by two different branches of solutions. In the limit of a small lateral confinement we obtain approximated solutions for the two branches and characterize the transition between them. Notably, the transition occurs when the pressure drop in the chamber is maximized. Furthermore, we solve our model numerically and show that this maximum pressure behaves nonmonotonically as a function of the lateral compression.
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Affiliation(s)
- Oz Oshri
- Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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8
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Liu Q, Wang W, Reynolds MF, Cao MC, Miskin MZ, Arias TA, Muller DA, McEuen PL, Cohen I. Micrometer-sized electrically programmable shape-memory actuators for low-power microrobotics. Sci Robot 2021; 6:6/52/eabe6663. [PMID: 34043551 DOI: 10.1126/scirobotics.abe6663] [Citation(s) in RCA: 36] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2020] [Accepted: 02/18/2021] [Indexed: 12/29/2022]
Abstract
Shape-memory actuators allow machines ranging from robots to medical implants to hold their form without continuous power, a feature especially advantageous for situations where these devices are untethered and power is limited. Although previous work has demonstrated shape-memory actuators using polymers, alloys, and ceramics, the need for micrometer-scale electro-shape-memory actuators remains largely unmet, especially ones that can be driven by standard electronics (~1 volt). Here, we report on a new class of fast, high-curvature, low-voltage, reconfigurable, micrometer-scale shape-memory actuators. They function by the electrochemical oxidation/reduction of a platinum surface, creating a strain in the oxidized layer that causes bending. They bend to the smallest radius of curvature of any electrically controlled microactuator (~500 nanometers), are fast (<100-millisecond operation), and operate inside the electrochemical window of water, avoiding bubble generation associated with oxygen evolution. We demonstrate that these shape-memory actuators can be used to create basic electrically reconfigurable microscale robot elements including actuating surfaces, origami-based three-dimensional shapes, morphing metamaterials, and mechanical memory elements. Our shape-memory actuators have the potential to enable the realization of adaptive microscale structures, bio-implantable devices, and microscopic robots.
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Affiliation(s)
- Qingkun Liu
- Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY 14853, USA.
| | - Wei Wang
- Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY 14853, USA.,Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
| | - Michael F Reynolds
- Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY 14853, USA
| | - Michael C Cao
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA
| | - Marc Z Miskin
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA
| | - Tomas A Arias
- Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY 14853, USA
| | - David A Muller
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA.,Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY 14853, USA
| | - Paul L McEuen
- Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY 14853, USA. .,Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY 14853, USA
| | - Itai Cohen
- Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY 14853, USA. .,Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY 14853, USA
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9
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Fan Chiang HC, Chiu LJ, Li HH, Hsiao PY, Hong TM. Crumpling an elastoplastic thin sphere. Phys Rev E 2021; 103:012209. [PMID: 33601503 DOI: 10.1103/physreve.103.012209] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2019] [Accepted: 12/23/2020] [Indexed: 11/07/2022]
Abstract
The phenomenon of crumpling is common in nature and our daily life. However, most of its properties, such as the power-law relation for pressure versus density and the ratio of bending and stretching energies, as well as the interesting statistical properties, were obtained by using flat sheets. This is in contrast to the fact that the majority of crumpled objects in the real world are three-dimensional. Notable examples are car wreckage, crushed aluminum cans, and blood cells that move through tissues constantly. In this work, we did a thorough examination of the properties of a crumpled spherical shell, hemisphere, cube, and cylinder via experiments and molecular-dynamics simulations. Physical arguments are provided to understand the discrepancies with those for flat sheets. The root of this disparity is found to lie less in the nonzero curvature, sharp edges and corner, and open boundary than in the dimensionality of the sample.
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Affiliation(s)
- Hung-Chieh Fan Chiang
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Li-Jie Chiu
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Hsin-Huei Li
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Pai-Yi Hsiao
- Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
| | - Tzay-Ming Hong
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan, Republic of China
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10
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Babaei M, Gao J, Clement A, Dayal K, Shankar MR. Torque-dense photomechanical actuation. SOFT MATTER 2021; 17:1258-1266. [PMID: 33283820 DOI: 10.1039/d0sm01352h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Contactless actuation powered using light is shown to generate torque densities approaching 10 N m kg-1 at angular velocities ∼102 rad s-1: metrics that compare favorably against tethered electromechanical systems. This is possible even though the extinction of actinic light limits the characteristic thickness of photoresponse in polymers to tens of μm. Confinement of molecularly patterned developable shells fabricated from azobenzene-functionalized liquid crystalline polymers encodes torque-dense photoactuation. Photostrain gradients from unstructured irradiation segment this geometry into two oppositely curved regions connected by a curved crease. A monolithic curved shell spontaneously bifurcates into a jointed, arm-like mechanism that generates flexure over sweep angles exceeding a radian. Strain focusing at the crease is hierarchical: an integral crease nucleates at smaller magnitudes of the prebiased curvature, while a crease decorated with point-like defects emerges at larger curvatures. The phase-space of morphogenesis is traceable to the competition between stretch and bending energies and is parameterizable as a function of the geometry. The framework for generating repetitive torque-dense actuation from slender light-powered actuators holds broader implications for the design of soft, remotely operated machines. Here, it is harnessed in illustrative mechanisms including levers, lifters and grabbers that are powered and regulated exclusively using light.
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Affiliation(s)
- Mahnoush Babaei
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA
| | - Junfeng Gao
- Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA.
| | - Arul Clement
- Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA.
| | - Kaushik Dayal
- Department of Civil and Environmental Engineering and Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA, USA
| | - M Ravi Shankar
- Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA.
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11
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Kernes J, Levine AJ. Effects of curvature on the propagation of undulatory waves in lower dimensional elastic materials. Phys Rev E 2021; 103:013002. [PMID: 33601515 DOI: 10.1103/physreve.103.013002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 12/16/2020] [Indexed: 06/12/2023]
Abstract
The mechanics of lower dimensional elastic structures depends strongly on the geometry of their stress-free state. Elastic deformations separate into in-plane stretching and lower energy out-of-plane bending deformations. For elastic structures with a curved stress-free state, these two elastic modes are coupled within linear elasticity. We investigate the effect of that curvature-induced coupling on wave propagation in lower dimensional elastic structures, focusing on the simplest example-a curved elastic rod in two dimensions. We focus only on the geometry-induced coupling between bending and longitudinal (in-plane) strain that is common to both rods in two dimensions and to elastic shells. We find that the dispersion relation of the waves becomes gapped in the presence of finite curvature; bending modes are absent below a frequency proportional to the curvature of the rod. By studying the scattering of undulatory waves off regions of uniform curvature, we find that undulatory waves with frequencies in the gap associated with the curved region tunnel through that curved region via conversion into compression waves. These results should be directly applicable to the spectrum and spatial distribution of phonon modes in a number of curved rod-like elastic solids, including carbon nanotubes and biopolymer filaments.
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Affiliation(s)
- Jonathan Kernes
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA
| | - Alex J Levine
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1596, USA
- Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1596, USA
- Department of Computational Medicine, UCLA, Los Angeles, California 90095-1596, USA
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12
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Waitukaitis S, Dieleman P, van Hecke M. Non-Euclidean origami. Phys Rev E 2020; 102:031001. [PMID: 33075898 DOI: 10.1103/physreve.102.031001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2019] [Accepted: 08/31/2020] [Indexed: 11/07/2022]
Abstract
Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex.
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Affiliation(s)
- Scott Waitukaitis
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Peter Dieleman
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | - Martin van Hecke
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
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13
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Gorissen B, Melancon D, Vasios N, Torbati M, Bertoldi K. Inflatable soft jumper inspired by shell snapping. Sci Robot 2020; 5:5/42/eabb1967. [DOI: 10.1126/scirobotics.abb1967] [Citation(s) in RCA: 71] [Impact Index Per Article: 17.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2020] [Accepted: 04/08/2020] [Indexed: 12/20/2022]
Abstract
Fluidic soft actuators are enlarging the robotics toolbox by providing flexible elements that can display highly complex deformations. Although these actuators are adaptable and inherently safe, their actuation speed is typically slow because the influx of fluid is limited by viscous forces. To overcome this limitation and realize soft actuators capable of rapid movements, we focused on spherical caps that exhibit isochoric snapping when pressurized under volume-controlled conditions. First, we noted that this snap-through instability leads to both a sudden release of energy and a fast cap displacement. Inspired by these findings, we investigated the response of actuators that comprise such spherical caps as building blocks and observed the same isochoric snapping mechanism upon inflation. Last, we demonstrated that this instability can be exploited to make these actuators jump even when inflated at a slow rate. Our study provides the foundation for the design of an emerging class of fluidic soft devices that can convert a slow input signal into a fast output deformation.
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Affiliation(s)
- Benjamin Gorissen
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - David Melancon
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - Nikolaos Vasios
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - Mehdi Torbati
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - Katia Bertoldi
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138, USA
- Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA 02138, USA
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14
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Berry M, Lee-Trimble ME, Santangelo CD. Topological transitions in the configuration space of non-Euclidean origami. Phys Rev E 2020; 101:043003. [PMID: 32422808 DOI: 10.1103/physreve.101.043003] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2019] [Accepted: 03/16/2020] [Indexed: 06/11/2023]
Abstract
Origami structures have been proposed as a means of creating three-dimensional structures from the micro- to the macroscale and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding of the kinematics of origami fold patterns. Here we study the configurations of non-Euclidean origami, folding structures with Gaussian curvature concentrated on the vertices, for arbitrary origami fold patterns. The kinematics of such structures depends crucially on the sign of the Gaussian curvature. As an application of our general results, we show that the configuration space of nonintersecting, oriented vertices with positive Gaussian curvature decomposes into disconnected subspaces; there is no pathway between them without tearing the origami. In contrast, the configuration space of negative Gaussian curvature vertices remains connected. This provides a new, and only partially explored, mechanism by which the mechanics and folding of an origami structure could be controlled.
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Affiliation(s)
- M Berry
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - M E Lee-Trimble
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - C D Santangelo
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA and Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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Charpentier V, Adriaenssens S. Effect of Gravity on the Scale of Compliant Shells. Biomimetics (Basel) 2020; 5:biomimetics5010004. [PMID: 32012708 PMCID: PMC7148455 DOI: 10.3390/biomimetics5010004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2019] [Revised: 12/28/2019] [Accepted: 01/09/2020] [Indexed: 11/16/2022] Open
Abstract
Thin shells are found across scales ranging from biological blood cells to engineered large-span roof structures. The engineering design of thin shells used as mechanisms has occasionally been inspired by biomimetic concept generators. The research goal of this paper is to establish the physical limits of scalability of shells. Sixty-four instances of shells across length scales have been organized into five categories: engineering stiff and compliant, plant compliant, avian egg stiff, and micro-scale compliant shells. Based on their thickness and characteristic dimensions, the mechanical behavior of these 64 shells can be characterized as 3D solids, thick or thin shells, or membranes. Two non-dimensional indicators, the Föppl–von Kármán number and a novel indicator, namely the gravity impact number, are adopted to establish the scalability limits of these five categories. The results show that these shells exhibit similar mechanical behavior across scales. As a result, micro-scale shell geometries found in biology, can be upscaled to engineered shell geometries. However, as the characteristic shell dimension increases, gravity (and its associated loading) becomes a hindrance to the adoption of thin shells as compliant mechanisms at the larger scales-the physical limit of compliance in the scaling of thin shells is found to be around 0.1 m.
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Dorsey KJ, Pearson TG, Esposito E, Russell S, Bircan B, Han Y, Miskin MZ, Muller DA, Cohen I, McEuen PL. Atomic Layer Deposition for Membranes, Metamaterials, and Mechanisms. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2019; 31:e1901944. [PMID: 31148291 DOI: 10.1002/adma.201901944] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2019] [Revised: 05/03/2019] [Indexed: 05/19/2023]
Abstract
Bending and folding techniques such as origami and kirigami enable the scale-invariant design of 3D structures, metamaterials, and robots from 2D starting materials. These design principles are especially valuable for small systems because most micro- and nanofabrication involves lithographic patterning of planar materials. Ultrathin films of inorganic materials serve as an ideal substrate for the fabrication of flexible microsystems because they possess high intrinsic strength, are not susceptible to plasticity, and are easily integrated into microfabrication processes. Here, atomic layer deposition (ALD) is employed to synthesize films down to 2 nm thickness to create membranes, metamaterials, and machines with micrometer-scale dimensions. Two materials are studied as model systems: ultrathin SiO2 and Pt. In this thickness limit, ALD films of these materials behave elastically and can be fabricated with fJ-scale bending stiffnesses. Further, ALD membranes are utilized to design micrometer-scale mechanical metamaterials and magnetically actuated 3D devices. These results establish thin ALD films as a scalable basis for micrometer-scale actuators and robotics.
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Affiliation(s)
- Kyle J Dorsey
- School of Applied and Engineering Physics, Cornell University, 271 Clark Hall, Ithaca, NY, 14853, USA
| | - Tanner G Pearson
- School of Applied and Engineering Physics, Cornell University, 271 Clark Hall, Ithaca, NY, 14853, USA
| | - Edward Esposito
- Laboratory of Atomic and Solid State Physics, Cornell University, 511 Clark Hall, Ithaca, NY, 14853, USA
| | - Sierra Russell
- College of Nanoscale Sciences, SUNY Polytechnic Institute, 247 Fuller Road, Albany, NY, 12203, USA
| | - Baris Bircan
- School of Applied and Engineering Physics, Cornell University, 271 Clark Hall, Ithaca, NY, 14853, USA
| | - Yimo Han
- School of Applied and Engineering Physics, Cornell University, 271 Clark Hall, Ithaca, NY, 14853, USA
| | - Marc Z Miskin
- Laboratory of Atomic and Solid State Physics, Cornell University, 511 Clark Hall, Ithaca, NY, 14853, USA
- Kavli Institute for Nanoscale Science, Cornell University, 420 Physical Sciences Building, Ithaca, NY, 14853, USA
| | - David A Muller
- School of Applied and Engineering Physics, Cornell University, 271 Clark Hall, Ithaca, NY, 14853, USA
- Kavli Institute for Nanoscale Science, Cornell University, 420 Physical Sciences Building, Ithaca, NY, 14853, USA
| | - Itai Cohen
- Laboratory of Atomic and Solid State Physics, Cornell University, 511 Clark Hall, Ithaca, NY, 14853, USA
- Kavli Institute for Nanoscale Science, Cornell University, 420 Physical Sciences Building, Ithaca, NY, 14853, USA
| | - Paul L McEuen
- Laboratory of Atomic and Solid State Physics, Cornell University, 511 Clark Hall, Ithaca, NY, 14853, USA
- Kavli Institute for Nanoscale Science, Cornell University, 420 Physical Sciences Building, Ithaca, NY, 14853, USA
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18
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Bende NP, Yu T, Corbin NA, Dias MA, Santangelo CD, Hanna JA, Hayward RC. Overcurvature induced multistability of linked conical frusta: how a 'bendy straw' holds its shape. SOFT MATTER 2018; 14:8636-8642. [PMID: 30334045 DOI: 10.1039/c8sm01355a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the origins of multiple mechanically stable states exhibited by an elastic shell comprising multiple conical frusta, a geometry common to reconfigurable corrugated structures such as 'bendy straws'. This multistability is characterized by mechanical stability of axially extended and collapsed states, as well as a partially inverted 'bent' state that exhibits stability in any azimuthal direction. To understand the origin of this behavior, we study how geometry and internal stress affect the stability of linked conical frusta. We find that tuning geometrical parameters such as the frustum heights and cone angles can provide axial bistability, whereas stability in the bent state requires a sufficient amount of internal pre-stress, resulting from a mismatch between the natural and geometric curvatures of the shell. We provide insight into the latter effect through curvature analysis during deformation using X-ray computed tomography (CT), and with a simple mechanical model that captures the qualitative behavior of these highly reconfigurable systems.
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Affiliation(s)
- Nakul P Bende
- Polymer Science and Engineering, University of Massachusetts Amherst, MA, USA.
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20
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Zhang C, Hao YK, Li B, Feng XQ, Gao H. Wrinkling patterns in soft shells. SOFT MATTER 2018; 14:1681-1688. [PMID: 29419847 DOI: 10.1039/c7sm02261a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Curvature plays an important role in the morphological evolution of soft shells under stretch. Here, through a combination of experiment, theory and simulation, we investigate the behavior of a hemispherical soft shell subject to an increasing outward point force at its pole. In contrast to an inward point force inducing a polygonal pattern of buckling in the shell, we observe a four-stage morphological transition and symmetry breaking under an increasing outward point force. The shell undergoes axisymmetric deformation around its pole and then buckles into a non-axisymmetric shape with a number of shallow wrinkles emanating from the pole, followed by the emergence of crater-like deep crumples and ultimately a transformation into a wrinkled pseudocone. Our theoretical analysis and numerical simulations yield the critical conditions for the morphological transitions at each stage of deformation and reveal the underlying interplays between elastic bending and stretching energies and the curvature of the shell.
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Affiliation(s)
- Cheng Zhang
- Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
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21
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Sano TG, Wada H. Snap-buckling in asymmetrically constrained elastic strips. Phys Rev E 2018; 97:013002. [PMID: 29448364 DOI: 10.1103/physreve.97.013002] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Indexed: 11/07/2022]
Abstract
When a flat elastic strip is compressed along its axis, it is bent in one of two possible directions via spontaneous symmetry breaking, forming a cylindrical arc. This is a phenomenon well known as Euler buckling. When this cylindrical section is pushed in the other direction, the bending direction can suddenly reverse. This instability is called "snap-through buckling" and is one of the elementary shape transitions in a prestressed thin structure. Combining experiments and theory, we study snap-buckling of an elastic strip with one end hinged and the other end clamped. These asymmetric boundary constraints break the intrinsic symmetry of the strip, generating mechanical behaviors, including largely hysteretic but reproducible force responses and switchlike discontinuous shape changes. We establish the set of exact analytical solutions to fully explain all our major experimental and numerical findings. Asymmetric boundary conditions arise naturally in diverse situations when a thin object is in contact with a solid surface at one end. The introduction of asymmetry through boundary conditions yields new insight into complex and programmable functionalities in material and industrial design.
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Affiliation(s)
- Tomohiko G Sano
- Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan.,Research Organization of Science and Technology, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
| | - Hirofumi Wada
- Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
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22
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Ambulo CP, Burroughs JJ, Boothby JM, Kim H, Shankar MR, Ware TH. Four-dimensional Printing of Liquid Crystal Elastomers. ACS APPLIED MATERIALS & INTERFACES 2017; 9:37332-37339. [PMID: 28967260 DOI: 10.1021/acsami.7b11851] [Citation(s) in RCA: 190] [Impact Index Per Article: 27.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
Three-dimensional structures capable of reversible changes in shape, i.e., four-dimensional-printed structures, may enable new generations of soft robotics, implantable medical devices, and consumer products. Here, thermally responsive liquid crystal elastomers (LCEs) are direct-write printed into 3D structures with a controlled molecular order. Molecular order is locally programmed by controlling the print path used to build the 3D object, and this order controls the stimulus response. Each aligned LCE filament undergoes 40% reversible contraction along the print direction on heating. By printing objects with controlled geometry and stimulus response, magnified shape transformations, for example, volumetric contractions or rapid, repetitive snap-through transitions, are realized.
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Affiliation(s)
- Cedric P Ambulo
- Department of Bioengineering, The University of Texas at Dallas , Richardson, Texas 75080, United States
| | - Julia J Burroughs
- Department of Bioengineering, The University of Texas at Dallas , Richardson, Texas 75080, United States
| | - Jennifer M Boothby
- Department of Bioengineering, The University of Texas at Dallas , Richardson, Texas 75080, United States
| | - Hyun Kim
- Department of Bioengineering, The University of Texas at Dallas , Richardson, Texas 75080, United States
| | - M Ravi Shankar
- Department of Industrial Engineering, The University of Pittsburgh , Pittsburgh, Pennsylvania 15261, United States
| | - Taylor H Ware
- Department of Bioengineering, The University of Texas at Dallas , Richardson, Texas 75080, United States
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23
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Al Mosleh S, Santangelo C. Nonlinear mechanics of rigidifying curves. Phys Rev E 2017; 96:013003. [PMID: 29347169 DOI: 10.1103/physreve.96.013003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2017] [Indexed: 06/07/2023]
Abstract
Thin shells are characterized by a high cost of stretching compared to bending. As a result isometries of the midsurface of a shell play a crucial role in their mechanics. In turn, curves on the midsurface with zero normal curvature play a critical role in determining the number and behavior of isometries. In this paper, we show how the presence of these curves results in a decrease in the number of linear isometries. Paradoxically, shells are also known to continuously fold more easily across these rigidifying curves than other curves on the surface. We show how including nonlinearities in the strain can explain these phenomena and demonstrate folding isometries with explicit solutions to the nonlinear isometry equations. In addition to explicit solutions, exact geometric arguments are given to validate and guide our analysis in a coordinate-free way.
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Affiliation(s)
- Salem Al Mosleh
- Physics Department, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
| | - Christian Santangelo
- Physics Department, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
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24
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Abstract
Cell shapes are related to their biological function. More generally, membrane morphology plays a role in the segregation and activity of transmembrane proteins. Here we show geometric implications regarding how cellular mechanics plays a role in localizing thermal fluctuations on the membrane. We show theoretically that certain geometric features of curved shells control the spatial distribution of membrane undulations. We experimentally verify this theory using discocyte red blood cells and find that geometry alone is sufficient to account for the observed spatial distribution of fluctuations. Our results, based on statistical physics and membrane elasticity, have general implications for the use of membrane shape to control thermal undulations in a variety of nanostructured materials ranging from cell membranes to graphene sheets. The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, “singular lines,” leads to a breakdown of linear membrane theory. As a result, these geometric curves effectively partition the cell into regions whose fluctuations are only weakly coupled. We validate these predictions using high-resolution microscopy of human red blood cells (RBCs) as a case study. Our observations show geometry-dependent localization of thermal fluctuations consistent with our theoretical modeling, demonstrating the efficacy in combining shell theory with equilibrium statistical physics for describing the thermalized morphology of cellular membranes.
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25
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Folding to Curved Surfaces: A Generalized Design Method and Mechanics of Origami-based Cylindrical Structures. Sci Rep 2016; 6:33312. [PMID: 27624892 PMCID: PMC5022034 DOI: 10.1038/srep33312] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2016] [Accepted: 08/24/2016] [Indexed: 11/09/2022] Open
Abstract
Origami structures enrich the field of mechanical metamaterials with the ability to convert morphologically and systematically between two-dimensional (2D) thin sheets and three-dimensional (3D) spatial structures. In this study, an in-plane design method is proposed to approximate curved surfaces of interest with generalized Miura-ori units. Using this method, two combination types of crease lines are unified in one reprogrammable procedure, generating multiple types of cylindrical structures. Structural completeness conditions of the finite-thickness counterparts to the two types are also proposed. As an example of the design method, the kinematics and elastic properties of an origami-based circular cylindrical shell are analysed. The concept of Poisson’s ratio is extended to the cylindrical structures, demonstrating their auxetic property. An analytical model of rigid plates linked by elastic hinges, consistent with numerical simulations, is employed to describe the mechanical response of the structures. Under particular load patterns, the circular shells display novel mechanical behaviour such as snap-through and limiting folding positions. By analysing the geometry and mechanics of the origami structures, we extend the design space of mechanical metamaterials and provide a basis for their practical applications in science and engineering.
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26
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Haas PA, Goldstein RE. Elasticity and glocality: initiation of embryonic inversion in Volvox. J R Soc Interface 2016; 12:rsif.2015.0671. [PMID: 26490631 PMCID: PMC4685841 DOI: 10.1098/rsif.2015.0671] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are glocal, set by a complicated balance between local properties and global geometric constraints. Here, we explore this interplay during the inversion process of the green alga Volvox, whose embryos must turn themselves inside out to complete their development. This process has recently been shown to be well described by the deformations of an elastic shell under local variations of its intrinsic curvatures and stretches, although the detailed mechanics of the process have remained unclear. Through a combination of asymptotic analysis and numerical studies of the bifurcation behaviour, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.
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Affiliation(s)
- Pierre A Haas
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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27
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Raney JR, Nadkarni N, Daraio C, Kochmann DM, Lewis JA, Bertoldi K. Stable propagation of mechanical signals in soft media using stored elastic energy. Proc Natl Acad Sci U S A 2016; 113:9722-7. [PMID: 27519797 PMCID: PMC5024640 DOI: 10.1073/pnas.1604838113] [Citation(s) in RCA: 90] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals. Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.
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Affiliation(s)
- Jordan R Raney
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138; Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138
| | - Neel Nadkarni
- Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125
| | - Chiara Daraio
- Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125; Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
| | - Dennis M Kochmann
- Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125;
| | - Jennifer A Lewis
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138; Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138;
| | - Katia Bertoldi
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138; Kavli Institute, Harvard University, Cambridge, MA 02138
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28
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Abstract
Thin vegetal shells have recently been a significant source of inspiration for the design of smart materials and soft actuators. Herein is presented a novel analytical family of isometric deformations with a family of θ-folds crossing a family of parallel z-folds; it contains the isometric deformations of a banana-shaped surface inspired by a seedpod, which converts a vertical closing into either an horizontal closing or an opening depending on the location of the fold. Similarly to the seedpod, optimum shapes for opening ease are the most elongated ones.
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Affiliation(s)
- Etienne Couturier
- Laboratoire 'Matiere et Systemes Complexes' (MSC), UMR 7057 CNRS , Université Paris 7 Diderot , 75205 Paris Cedex 13, France
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29
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Fabrication of slender elastic shells by the coating of curved surfaces. Nat Commun 2016; 7:11155. [PMID: 27040377 PMCID: PMC4822016 DOI: 10.1038/ncomms11155] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2015] [Accepted: 02/26/2016] [Indexed: 11/08/2022] Open
Abstract
Various manufacturing techniques exist to produce double-curvature shells, including injection, rotational and blow molding, as well as dip coating. However, these industrial processes are typically geared for mass production and are not directly applicable to laboratory research settings, where adaptable, inexpensive and predictable prototyping tools are desirable. Here, we study the rapid fabrication of hemispherical elastic shells by coating a curved surface with a polymer solution that yields a nearly uniform shell, upon polymerization of the resulting thin film. We experimentally characterize how the curing of the polymer affects its drainage dynamics and eventually selects the shell thickness. The coating process is then rationalized through a theoretical analysis that predicts the final thickness, in quantitative agreement with experiments and numerical simulations of the lubrication flow field. This robust fabrication framework should be invaluable for future studies on the mechanics of thin elastic shells and their intrinsic geometric nonlinearities.
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30
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Silverberg JL, Na JH, Evans AA, Liu B, Hull TC, Santangelo CD, Lang RJ, Hayward RC, Cohen I. Origami structures with a critical transition to bistability arising from hidden degrees of freedom. NATURE MATERIALS 2015; 14:389-93. [PMID: 25751075 DOI: 10.1038/nmat4232] [Citation(s) in RCA: 138] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2014] [Accepted: 01/30/2015] [Indexed: 05/24/2023]
Abstract
Origami is used beyond purely aesthetic pursuits to design responsive and customizable mechanical metamaterials. However, a generalized physical understanding of origami remains elusive, owing to the challenge of determining whether local kinematic constraints are globally compatible and to an incomplete understanding of how the folded sheet's material properties contribute to the overall mechanical response. Here, we show that the traditional square twist, whose crease pattern has zero degrees of freedom (DOF) and therefore should not be foldable, can nevertheless be folded by accessing bending deformations that are not explicit in the crease pattern. These hidden bending DOF are separated from the crease DOF by an energy gap that gives rise to a geometrically driven critical bifurcation between mono- and bistability. Noting its potential utility for fabricating mechanical switches, we use a temperature-responsive polymer-gel version of the square twist to demonstrate hysteretic folding dynamics at the sub-millimetre scale.
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Affiliation(s)
| | - Jun-Hee Na
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Arthur A Evans
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Bin Liu
- Physics Department, Cornell University, Ithaca, New York 14853, USA
| | - Thomas C Hull
- Department of Mathematics, Western New England University, Springfield, Massachusetts 01119, USA
| | | | | | - Ryan C Hayward
- Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Itai Cohen
- Physics Department, Cornell University, Ithaca, New York 14853, USA
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