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Shankar S, Nelson DR. Thermalized buckling of isotropically compressed thin sheets. Phys Rev E 2021; 104:054141. [PMID: 34942813 DOI: 10.1103/physreve.104.054141] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 10/19/2021] [Indexed: 11/07/2022]
Abstract
The buckling of thin elastic sheets is a classic mechanical instability that occurs over a wide range of scales. In the extreme limit of atomically thin membranes like graphene, thermal fluctuations can dramatically modify such mechanical instabilities. We investigate here the delicate interplay of boundary conditions, nonlinear mechanics, and thermal fluctuations in controlling buckling of confined thin sheets under isotropic compression. We identify two inequivalent mechanical ensembles based on the boundaries at constant strain (isometric) or at constant stress (isotensional) conditions. Remarkably, in the isometric ensemble, boundary conditions induce a novel long-ranged nonlinear interaction between the local tilt of the surface at distant points. This interaction combined with a spontaneously generated thermal tension leads to a renormalization group description of two distinct universality classes for thermalized buckling, realizing a mechanical variant of Fisher-renormalized critical exponents. We formulate a complete scaling theory of buckling as an unusual phase transition with a size-dependent critical point, and we discuss experimental ramifications for the mechanical manipulation of ultrathin nanomaterials.
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Affiliation(s)
- Suraj Shankar
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - David R Nelson
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.,Department of Molecular and Cellular Biology and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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Siéfert E, Cattaud N, Reyssat E, Roman B, Bico J. Stretch-Induced Bending of Soft Ribbed Strips. PHYSICAL REVIEW LETTERS 2021; 127:168002. [PMID: 34723608 DOI: 10.1103/physrevlett.127.168002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Revised: 07/01/2021] [Accepted: 08/31/2021] [Indexed: 06/13/2023]
Abstract
We show that ribbed elastic strips under tension present large spontaneous curvature and may close into tubes. In this single material architectured system, transverse bending results from a bilayer effect induced by Poisson contraction as the textured ribbon is stretched. Surprisingly, the induced curvature may reverse if ribs of different orientations are considered. Slender ribbed structures may also undergo a nontrivial buckling transition. We use analytical calculations to describe the evolution of the morphology of the ribbon and the transitions between the different experimental regimes as a function of material properties, geometrical parameters, and stretching strain. This scale-independent phenomenon may help the manufacturing of tubular textured structures or easily controllable grippers at small scale.
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Affiliation(s)
- Emmanuel Siéfert
- Nonlinear Physical Chemistry Unit, Universit Libre de Bruxelles, B-1050 Bruxelles, Belgium
| | - Nicolas Cattaud
- Laboratoire de Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Etienne Reyssat
- Laboratoire de Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Benoît Roman
- Laboratoire de Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - José Bico
- Laboratoire de Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005 Paris, France
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Barois T, Jalisse I, Tadrist L, Virot E. Transition to stress focusing for locally curved sheets. Phys Rev E 2021; 104:014801. [PMID: 34412236 DOI: 10.1103/physreve.104.014801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2021] [Accepted: 06/04/2021] [Indexed: 11/07/2022]
Abstract
A rectangular thin elastic sheet is deformed by forcing a contact between two points at the middle of its length. A transition to buckling with stress focusing is reported for the sheets sufficiently narrow with a critical width proportional to the sheet length with an exponent 2/3 in the small thickness limit. Additionally, a spring network model is solved to explore the thick sheet limit and to validate the scaling behavior of the transition in the thin sheet limit. The numerical results reveal that buckling does not exist for the thickest sheets, and a stability criterion is established for the buckling of a curved sheet.
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Affiliation(s)
- Thomas Barois
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Ilyes Jalisse
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Loïc Tadrist
- Aix-Marseille Univ., CNRS, ISM, Marseille, France
| | - Emmanuel Virot
- hap2U, 75 Avenue Gabriel Péri, 38400 Saint Martin d'Hères, France
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Mourran A, Jung O, Vinokur R, Möller M. Microgel that swims to the beat of light. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:79. [PMID: 34129113 PMCID: PMC8206062 DOI: 10.1140/epje/s10189-021-00084-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 05/27/2021] [Indexed: 05/04/2023]
Abstract
Complementary to the quickly advancing understanding of the swimming of microorganisms, we demonstrate rather simple design principles for systems that can mimic swimming by body shape deformation. For this purpose, we developed a microswimmer that could be actuated and controlled by fast temperature changes through pulsed infrared light irradiation. The construction of the microswimmer has the following features: (i) it is a bilayer ribbon with a length of 80 or 120 [Formula: see text]m, consisting of a thermo-responsive hydrogel of poly-N-isopropylamide coated with a 2-nm layer of gold and equipped with homogeneously dispersed gold nanorods; (ii) the width of the ribbon is linearly tapered with a wider end of 5 [Formula: see text]m and a tip of 0.5 [Formula: see text]m; (iii) a thickness of only 1 and 2 [Formula: see text]m that ensures a maximum variation of the cross section of the ribbon along its length from square to rectangular. These wedge-shaped ribbons form conical helices when the hydrogel is swollen in cold water and extend to a filament-like object when the temperature is raised above the volume phase transition of the hydrogel at [Formula: see text]. The two ends of these ribbons undergo different but coupled modes of motion upon fast temperature cycling through plasmonic heating of the gel-objects from inside. Proper choice of the IR-light pulse sequence caused the ribbons to move at a rate of 6 body length/s (500 [Formula: see text]m/s) with the wider end ahead. Within the confinement of rectangular container of 30 [Formula: see text]m height and 300 [Formula: see text]m width, the different modes can be actuated in a way that the movement is directed by the energy input between spinning on the spot and fast forward locomotion.
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Affiliation(s)
- Ahmed Mourran
- DWI - Leibniz-Institut for Interactive Materials, RWTH university, Forckenbeckstr. 50, D-52056, Aachen, Germany.
| | - Oliver Jung
- DWI - Leibniz-Institut for Interactive Materials, RWTH university, Forckenbeckstr. 50, D-52056, Aachen, Germany
| | - Rostislav Vinokur
- DWI - Leibniz-Institut for Interactive Materials, RWTH university, Forckenbeckstr. 50, D-52056, Aachen, Germany
| | - Martin Möller
- DWI - Leibniz-Institut for Interactive Materials, RWTH university, Forckenbeckstr. 50, D-52056, Aachen, Germany.
- Institut of Technical and Macromolecular Chemistry der RWTH Aachen, Forckenbeckstr. 50, D-52056, Aachen, Germany.
- 3 Max-Planck School Matter to life, D-69120, Heidelbergy, Germany.
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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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Li WB, Zhang WM, Zou HX, Peng ZK, Meng G. Bioinspired Variable Stiffness Dielectric Elastomer Actuators with Large and Tunable Load Capacity. Soft Robot 2019; 6:631-643. [DOI: 10.1089/soro.2018.0046] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- Wen-Bo Li
- State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
| | - Wen-Ming Zhang
- State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
| | - Hong-Xiang Zou
- State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
| | - Zhi-Ke Peng
- State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
| | - Guang Meng
- State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
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Taffetani M, Box F, Neveu A, Vella D. Limitations of curvature-induced rigidity: How a curved strip buckles under gravity. ACTA ACUST UNITED AC 2019. [DOI: 10.1209/0295-5075/127/14001] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Tadrist L, Darbois-Texier B. Are leaves optimally designed for self-support? An investigation on giant monocots. J Theor Biol 2016; 396:125-31. [PMID: 26920248 DOI: 10.1016/j.jtbi.2016.02.018] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2015] [Revised: 02/04/2016] [Accepted: 02/12/2016] [Indexed: 10/22/2022]
Abstract
Leaves are the organs that intercept light and create photosynthesis. Efficient light interception is provided by leaves oriented orthogonal to most of the sun rays. Except in the polar regions, this means orthogonal to the direction of acceleration due to gravity, or simply horizontal. The leaves of almost all terrestrial plants grow in a gravity field that tends to bend them downward and therefore may counteract light interception. Plants thus allocate biomass for self-support in order to maintain their leaves horizontal. To compete with other species (inter-species competition), as well as other individuals within the same species (intra-species competition), self-support must be achieved with the least biomass produced. This study examines to what extent leaves are designed to self-support. We show here that a basic mechanical model provides the optimal dimensions of a leaf for light interception and self-support. These results are compared to measurements made on leaves of various giant monocot species, especially palm trees and banana trees. The comparison between experiments and model predictions shows that the longer palms are optimally designed for self-support whereas shorter leaves are shaped predominantly by other parameters of selection.
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Affiliation(s)
- Loïc Tadrist
- LadHyX, Department of Mechanics, École Polytechnique-CNRS, 91128 Palaiseau, France; Microfluidics Lab, Department of Aerospace and Mechanics, University of Liège, Liège 4000, Belgium.
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