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Yang Y, Read H, Sbai M, Zareei A, Forte AE, Melancon D, Bertoldi K. Complex Deformation in Soft Cylindrical Structures via Programmable Sequential Instabilities. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024:e2406611. [PMID: 39240015 DOI: 10.1002/adma.202406611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2024] [Revised: 07/23/2024] [Indexed: 09/07/2024]
Abstract
The substantial deformation exhibited by hyperelastic cylindrical shells under pressurization makes them an ideal platform for programmable inflatable structures. If negative pressure is applied, the cylindrical shell will buckle, leading to a sequence of rich deformation modes, all of which are fully recoverable due to the hyperelastic material choice. While the initial buckling event under vacuum is well understood, here, the post-buckling regime is explored and a region in the design space is identified in which a coupled twisting-contraction deformation mode occurs; by carefully controlling the geometry of our homogeneous shells, the proportion of contraction versus twist can be controlled. Additionally, bending as a post-buckling deformation mode can be unlocked by varying the thickness of our shells across the circumference. Since these soft shells can fully recover from substantial deformations caused by buckling, then these instability-driven deformations are harnessed to build soft machines capable of a programmable sequence of movements with a single actuation input.
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Affiliation(s)
- Yi Yang
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Helen Read
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Mohammed Sbai
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Ahmad Zareei
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Antonio Elia Forte
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Department of Engineering, King's College London, London, WC2R 2LS, UK
| | - David Melancon
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Department of Mechanical Engineering, Polytechnique Montreal, Quebec, H3T 1J4, Canada
| | - Katia Bertoldi
- J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
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2
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Shen J, Garrad M, Zhang Q, Wong VCH, Pirrera A, Groh RMJ. A rapid-response soft end effector inspired by the hummingbird beak. J R Soc Interface 2024; 21:20240148. [PMID: 39226926 DOI: 10.1098/rsif.2024.0148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Revised: 05/11/2024] [Accepted: 07/26/2024] [Indexed: 09/05/2024] Open
Abstract
Biology is a wellspring of inspiration in engineering design. This paper delves into the application of elastic instabilities-commonly used in biological systems to facilitate swift movement-as a power-amplification mechanism for soft robots. Specifically, inspired by the nonlinear mechanics of the hummingbird beak-and shedding further light on it-we design, build and test a novel, rapid-response, soft end effector. The hummingbird beak embodies the capacity for swift movement, achieving closure in less than [Formula: see text]. Previous work demonstrated that rapid movement is achieved through snap-through deformations, induced by muscular actuation of the beak's root. Using nonlinear finite element simulations coupled with continuation algorithms, we unveil a representative portion of the equilibrium manifold of the beak-inspired structure. The exploration involves the application of a sequence of rotations as exerted by the hummingbird muscles. Specific emphasis is placed on pinpointing and tailoring the position along the manifold of the saddle-node bifurcation at which the onset of elastic instability triggers dynamic snap-through. We show the critical importance of the intermediate rotation input in the sequence, as it results in the accumulation of elastic energy that is then explosively released as kinetic energy upon snap-through. Informed by our numerical studies, we conduct experimental testing on a prototype end effector fabricated using a compliant material (thermoplastic polyurethane). The experimental results support the trends observed in the numerical simulations and demonstrate the effectiveness of the bio-inspired design. Specifically, we measure the energy transferred by the soft end effector to a pendulum, varying the input levels in the sequence of prescribed rotations. Additionally, we demonstrate a potential robotic application in scenarios demanding explosive action. From a mechanics perspective, our work sheds light on how pre-stress fields can enable swift movement in soft robotic systems with the potential to facilitate high input-to-output energy efficiency.
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Affiliation(s)
- Jiajia Shen
- Bristol Composites Institute (BCI), School of Civil, Aerospace and Design Engineering, University of Bristol , Bristol BS8 1TR, UK
- Exeter Technologies Group (ETG), Department of Engineering, University of Exeter , Exeter EX4 4PY, UK
| | - Martin Garrad
- Department of Engineering Mathematics, University of Bristol , Bristol BS8 1TR, UK
- SoftLab, Bristol Robotics Laboratory, University of Bristol and University of the West of England , Bristol BS8 1TR, UK
| | - Qicheng Zhang
- Faculty of Science and Engineering, Swansea University , Swansea SA1 8EN, UK
| | - Vico Chun Hei Wong
- Bristol Composites Institute (BCI), School of Civil, Aerospace and Design Engineering, University of Bristol , Bristol BS8 1TR, UK
| | - Alberto Pirrera
- Bristol Composites Institute (BCI), School of Civil, Aerospace and Design Engineering, University of Bristol , Bristol BS8 1TR, UK
| | - Rainer M J Groh
- Bristol Composites Institute (BCI), School of Civil, Aerospace and Design Engineering, University of Bristol , Bristol BS8 1TR, UK
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3
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Farago J, Jouanlanne M, Egelé A, Hourlier-Fargette A. Elastic ribbons in bubble columns: When elasticity, capillarity, and gravity govern equilibrium configurations. Phys Rev E 2024; 110:024803. [PMID: 39294956 DOI: 10.1103/physreve.110.024803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2024] [Accepted: 07/12/2024] [Indexed: 09/21/2024]
Abstract
Taking advantage of the competition between elasticity and capillarity has proven to be an efficient way to design structures by folding, bending, or assembling elastic objects in contact with liquid interfaces. Elastocapillary effects often occur at scales where gravity does not play an important role, such as in microfabrication processes. However, the influence of gravity can become significant at the desktop scale, which is relevant for numerous situations including model experiments used to provide a fundamental physics understanding, working at easily accessible scales. We focus here on the case of elastic ribbons placed in two-dimensional bubble columns: by introducing an elastic ribbon inside the central soap films of a staircase bubble structure in a square cross-section column, the deviation from Plateau's laws (capillarity-dominated case dictating the shape of usual foams) can be quantified as a function of the rigidity of the ribbon. For long ribbons, gravity cannot be neglected. We provide a detailed theoretical analysis of the ribbon profile, taking into account capillarity, elasticity, and gravity. We compute the total energy of the system and perform energy minimization under constraints, using Lagrangian mechanics. The model is then validated via a comparison with experiments with three different ribbon thicknesses.
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Wang Q, Giudici A, Huang W, Wang Y, Liu M, Tawfick S, Vella D. Transient Amplification of Broken Symmetry in Elastic Snap-Through. PHYSICAL REVIEW LETTERS 2024; 132:267201. [PMID: 38996296 DOI: 10.1103/physrevlett.132.267201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Accepted: 05/23/2024] [Indexed: 07/14/2024]
Abstract
A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural state as the ends are released. A standard linear stability analysis suggests that the arch becomes unstable to asymmetric perturbations. Surprisingly, our experiments show that this is not always the case: symmetric transitions are also observed. Using experiments, numerics, and a toy model, we show that the symmetry of the transition depends on the rate at which the ends are released, with sufficiently fast loading leading to symmetric snap-through. Our toy model reveals that this behavior is caused by a region of the system's state space in which any initial asymmetry is amplified. The system may not enter this region when loaded fast (hence remaining symmetric), but will traverse it for some interval of time when loaded slowly, causing a transient amplification of asymmetry. Our toy model suggests that this behavior is not unique to snapping arches, but rather can be observed in dynamical systems where both a saddle-node and a pitchfork bifurcation occur in close proximity.
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Affiliation(s)
| | | | | | | | - Mingchao Liu
- Mathematical Institute, University of Oxford, Woodstock Rd, Oxford OX2 6GG, United Kingdom
- School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
- Department of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, United Kingdom
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Kumar S, Tiwari I, Ortega-Jimenez VM, Dillman AR, He D, Hu Y, Bhamla MS. Reversible kink instability drives ultrafast jumping in nematodes and soft robots. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.06.07.598012. [PMID: 38915562 PMCID: PMC11195127 DOI: 10.1101/2024.06.07.598012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/26/2024]
Abstract
Entomopathogenic nematodes (EPNs) exhibit a bending-elastic instability, or kink, before becoming airborne, a feature hypothesized but not proven to enhance jumping performance. Here, we provide the evidence that this kink is crucial for improving launch performance. We demonstrate that EPNs actively modulate their aspect ratio, forming a liquid-latched closed loop over a slow timescale O (1 s), then rapidly open it O (10 µs), achieving heights of 20 body lengths (BL) and generating ∼ 10 4 W/Kg of power. Using jumping nematodes, a bio-inspired Soft Jumping Model (SoftJM), and computational simulations, we explore the mechanisms and implications of this kink. EPNs control their takeoff direction by adjusting their head position and center of mass, a mechanism verified through phase maps of jump directions in simulations and SoftJM experiments. Our findings reveal that the reversible kink instability at the point of highest curvature on the ventral side enhances energy storage using the nematode's limited muscular force. We investigated the impact of aspect ratio on kink instability and jumping performance using SoftJM, and quantified EPN cuticle stiffness with AFM, comparing it with C. elegans . This led to a stiffness-modified SoftJM design with a carbon fiber backbone, achieving jumps of ∼25 BL. Our study reveals how harnessing kink instabilities, a typical failure mode, enables bidirectional jumps in soft robots on complex substrates like sand, offering a novel approach for designing limbless robots for controlled jumping, locomotion, and even planetary exploration.
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Rigato A, Meng H, Chardes C, Runions A, Abouakil F, Smith RS, LeGoff L. A mechanical transition from tension to buckling underlies the jigsaw puzzle shape morphogenesis of histoblasts in the Drosophila epidermis. PLoS Biol 2024; 22:e3002662. [PMID: 38870210 PMCID: PMC11175506 DOI: 10.1371/journal.pbio.3002662] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 05/03/2024] [Indexed: 06/15/2024] Open
Abstract
The polygonal shape of cells in proliferating epithelia is a result of the tensile forces of the cytoskeletal cortex and packing geometry set by the cell cycle. In the larval Drosophila epidermis, two cell populations, histoblasts and larval epithelial cells, compete for space as they grow on a limited body surface. They do so in the absence of cell divisions. We report a striking morphological transition of histoblasts during larval development, where they change from a tensed network configuration with straight cell outlines at the level of adherens junctions to a highly folded morphology. The apical surface of histoblasts shrinks while their growing adherens junctions fold, forming deep lobules. Volume increase of growing histoblasts is accommodated basally, compensating for the shrinking apical area. The folded geometry of apical junctions resembles elastic buckling, and we show that the imbalance between the shrinkage of the apical domain of histoblasts and the continuous growth of junctions triggers buckling. Our model is supported by laser dissections and optical tweezer experiments together with computer simulations. Our analysis pinpoints the ability of histoblasts to store mechanical energy to a much greater extent than most other epithelial cell types investigated so far, while retaining the ability to dissipate stress on the hours time scale. Finally, we propose a possible mechanism for size regulation of histoblast apical size through the lateral pressure of the epidermis, driven by the growth of cells on a limited surface. Buckling effectively compacts histoblasts at their apical plane and may serve to avoid physical harm to these adult epidermis precursors during larval life. Our work indicates that in growing nondividing cells, compressive forces, instead of tension, may drive cell morphology.
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Affiliation(s)
- Annafrancesca Rigato
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR7249, Turing Center for Living Systems, Marseille, France
- Aix Marseille Univ, CNRS, IBDM UMR7288, Turing Center for Living Systems, Marseille, France
| | - Huicheng Meng
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR7249, Turing Center for Living Systems, Marseille, France
| | - Claire Chardes
- Aix Marseille Univ, CNRS, IBDM UMR7288, Turing Center for Living Systems, Marseille, France
| | - Adam Runions
- Department of Computer Science, University of Calgary, Calgary, Canada
| | - Faris Abouakil
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR7249, Turing Center for Living Systems, Marseille, France
| | - Richard S. Smith
- John Innes Centre, Norwich Research Park, Norwich, United Kingdom
| | - Loïc LeGoff
- Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel UMR7249, Turing Center for Living Systems, Marseille, France
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Wu L, Pasini D. Zero modes activation to reconcile floppiness, rigidity, and multistability into an all-in-one class of reprogrammable metamaterials. Nat Commun 2024; 15:3087. [PMID: 38600069 PMCID: PMC11006655 DOI: 10.1038/s41467-024-47180-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 03/15/2024] [Indexed: 04/12/2024] Open
Abstract
Existing mechanical metamaterials are typically designed to either withstand loads as a stiff structure, shape morph as a floppy mechanism, or trap energy as a multistable matter, distinct behaviours that correspond to three primary classes of macroscopic solids. Their stiffness and stability are sealed permanently into their architecture, mostly remaining immutable post-fabrication due to the invariance of zero modes. Here, we introduce an all-in-one reprogrammable class of Kagome metamaterials that enable the in-situ reprogramming of zero modes to access the apparently conflicting properties of all classes. Through the selective activation of metahinges via self-contact, their architecture can be switched to acquire on-demand rigidity, floppiness, or global multistability, bridging the seemingly uncrossable gap between structures, mechanisms, and multistable matters. We showcase the versatile generalizations of the metahinge and remarkable reprogrammability of zero modes for a range of properties including stiffness, mechanical signal guiding, buckling modes, phonon spectra, and auxeticity, opening a plethora of opportunities for all-in-one materials and devices.
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Affiliation(s)
- Lei Wu
- Department of Mechanical Engineering, McGill University, Montreal, Canada
| | - Damiano Pasini
- Department of Mechanical Engineering, McGill University, Montreal, Canada.
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8
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Yoshida K, Wada H. Indentation of an elastic arch on a frictional substrate: Pinning, unfolding, and snapping. Phys Rev E 2024; 109:045001. [PMID: 38755807 DOI: 10.1103/physreve.109.045001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 02/26/2024] [Indexed: 05/18/2024]
Abstract
In this study, we investigate the morphology and mechanics of a naturally curved elastic arch loaded at its center and frictionally supported at both ends on a flat, rigid substrate. Through systematic numerical simulations, we classify the observed behaviors of the arch into three configurations in terms of the arch geometry and the coefficient of static friction with the substrate. A linear theory is developed based on a planar elastica model combined with Amontons-Coulomb's frictional law, which quantitatively explains the numerically constructed phase diagram. The snapping transition of a loaded arch in a sufficiently large indentation regime, which involves a discontinuous force jump, is numerically observed. The proposed model problem enables a fully analytical investigation and demonstrates a rich variety of mechanical behaviors owing to the interplay among elasticity, geometry, and friction. This study provides a basis for understanding more common but complex systems, such as a cylindrical shell subjected to a concentrated load and simultaneously supported by frictional contact with surrounding objects.
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Affiliation(s)
- Keisuke Yoshida
- Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
| | - Hirofumi Wada
- Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
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9
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Mendoza Nava H, Holderied MW, Pirrera A, Groh RMJ. Buckling-induced sound production in the aeroelastic tymbals of Yponomeuta. Proc Natl Acad Sci U S A 2024; 121:e2313549121. [PMID: 38315846 PMCID: PMC10873622 DOI: 10.1073/pnas.2313549121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Accepted: 12/13/2023] [Indexed: 02/07/2024] Open
Abstract
The loss of elastic stability (buckling) can lead to catastrophic failure in the context of traditional engineering structures. Conversely, in nature, buckling often serves a desirable function, such as in the prey-trapping mechanism of the Venus fly trap (Dionaea muscipula). This paper investigates the buckling-enabled sound production in the wingbeat-powered (aeroelastic) tymbals of Yponomeuta moths. The hindwings of Yponomeuta possess a striated band of ridges that snap through sequentially during the up- and downstroke of the wingbeat cycle-a process reminiscent of cellular buckling in compressed slender shells. As a result, bursts of ultrasonic clicks are produced that deter predators (i.e. bats). Using various biological and mechanical characterization techniques, we show that wing camber changes during the wingbeat cycle act as the single actuation mechanism that causes buckling to propagate sequentially through each stria on the tymbal. The snap-through of each stria excites a bald patch of the wing's membrane, thereby amplifying sound pressure levels and radiating sound at the resonant frequencies of the patch. In addition, the interaction of phased tymbal clicks from the two wings enhances the directivity of the acoustic signal strength, suggesting an improvement in acoustic protection. These findings unveil the acousto-mechanics of Yponomeuta tymbals and uncover their buckling-driven evolutionary origin. We anticipate that through bioinspiration, aeroelastic tymbals will encourage novel developments in the context of multi-stable morphing structures, acoustic structural monitoring, and soft robotics.
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Affiliation(s)
- Hernaldo Mendoza Nava
- Bristol Composites Institute, School of Civil, Aerospace & Design Engineering, University of Bristol, BristolBS8 1TR, United Kingdom
| | - Marc W. Holderied
- School of Biological Sciences, University of Bristol, BristolBS8 1TQ, United Kingdom
| | - Alberto Pirrera
- Bristol Composites Institute, School of Civil, Aerospace & Design Engineering, University of Bristol, BristolBS8 1TR, United Kingdom
| | - Rainer M. J. Groh
- Bristol Composites Institute, School of Civil, Aerospace & Design Engineering, University of Bristol, BristolBS8 1TR, United Kingdom
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10
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Livne G, Gat S, Armon S, Bernheim-Groswasser A. Self-assembled active actomyosin gels spontaneously curve and wrinkle similar to biological cells and tissues. Proc Natl Acad Sci U S A 2024; 121:e2309125121. [PMID: 38175871 PMCID: PMC10786314 DOI: 10.1073/pnas.2309125121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 11/28/2023] [Indexed: 01/06/2024] Open
Abstract
Living systems adopt a diversity of curved and highly dynamic shapes. These diverse morphologies appear on many length scales, from cells to tissues and organismal scales. The common driving force for these dynamic shape changes are contractile stresses generated by myosin motors in the cell cytoskeleton, that converts chemical energy into mechanical work. A good understanding of how contractile stresses in the cytoskeleton arise into different three-dimensional (3D) shapes and what are the shape selection rules that determine their final configurations is still lacking. To obtain insight into the relevant physical mechanisms, we recreate the actomyosin cytoskeleton in vitro, with precisely controlled composition and initial geometry. A set of actomyosin gel discs, intrinsically identical but of variable initial geometry, dynamically self-organize into a family of 3D shapes, such as domes and wrinkled shapes, without the need for specific preprogramming or additional regulation. Shape deformation is driven by the spontaneous emergence of stress gradients driven by myosin and is encoded in the initial disc radius to thickness aspect ratio, which may indicate shaping scalability. Our results suggest that while the dynamical pathways may depend on the detailed interactions between the different microscopic components within the gel, the final selected shapes obey the general theory of elastic deformations of thin sheets. Altogether, our results emphasize the importance for the emergence of active stress gradients for buckling-driven shape deformations and provide insights on the mechanically induced spontaneous shape transitions in contractile active matter, revealing potential shared mechanisms with living systems across scales.
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Affiliation(s)
- Gefen Livne
- Department of Chemical Engineering, Ilse Katz Institute for Nanoscale Science and Technology, Ben Gurion University of the Negev, Beer-Sheva84105, Israel
| | - Shachar Gat
- Department of Chemical Engineering, Ilse Katz Institute for Nanoscale Science and Technology, Ben Gurion University of the Negev, Beer-Sheva84105, Israel
| | - Shahaf Armon
- Department of Physics, Weizmann Institute of Science, Rehovot76100, Israel
| | - Anne Bernheim-Groswasser
- Department of Chemical Engineering, Ilse Katz Institute for Nanoscale Science and Technology, Ben Gurion University of the Negev, Beer-Sheva84105, Israel
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11
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Tam R, Harris TJC. Reshaping the Syncytial Drosophila Embryo with Cortical Actin Networks: Four Main Steps of Early Development. Results Probl Cell Differ 2024; 71:67-90. [PMID: 37996673 DOI: 10.1007/978-3-031-37936-9_4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2023]
Abstract
Drosophila development begins as a syncytium. The large size of the one-cell embryo makes it ideal for studying the structure, regulation, and effects of the cortical actin cytoskeleton. We review four main steps of early development that depend on the actin cortex. At each step, dynamic remodelling of the cortex has specific effects on nuclei within the syncytium. During axial expansion, a cortical actomyosin network assembles and disassembles with the cell cycle, generating cytoplasmic flows that evenly distribute nuclei along the ovoid cell. When nuclei move to the cell periphery, they seed Arp2/3-based actin caps which grow into an array of dome-like compartments that house the nuclei as they divide at the cell cortex. To separate germline nuclei from the soma, posterior germ plasm induces full cleavage of mono-nucleated primordial germ cells from the syncytium. Finally, zygotic gene expression triggers formation of the blastoderm epithelium via cellularization and simultaneous division of ~6000 mono-nucleated cells from a single internal yolk cell. During these steps, the cortex is regulated in space and time, gains domain and sub-domain structure, and undergoes mesoscale interactions that lay a structural foundation of animal development.
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Affiliation(s)
- Rebecca Tam
- Department of Cell & Systems Biology, University of Toronto, Toronto, ON, Canada
| | - Tony J C Harris
- Department of Cell & Systems Biology, University of Toronto, Toronto, ON, Canada.
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12
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Godefroid J, Bouttes D, Marcellan A, Barthel E, Monteux C. Surface stress and shape relaxation of gelling droplets. SOFT MATTER 2023; 19:7787-7795. [PMID: 37791988 DOI: 10.1039/d3sm00533j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/05/2023]
Abstract
Solidification is a heterogeneous transformation from liquid to solid, which usually combines transport, phase transition and mechanical strain. Predicting the shapes resulting from such a complex process is fascinating and has a wide range of implications from morphogenesis in biological tissues to industrial processes. For soft solids initially at equilibrium, elastic stresses, whether tensile or compressive, can be induced by heterogeneous volumetric deformations of the material. These stresses trigger surface instabilities leading to variations of curvature and shape of the solids. In this article, we study the shape evolution of elongated droplets of polymer and particle suspensions undergoing a solidification process caused by the inward diffusion of a gelling agent from the surface. We show experimentally and numerically that there appears a layer of gelled material growing at the surface. Due to volume contraction, this layer induces tensile stresses and drives a flow in the ungelled liquid core, resulting in the relaxation of the droplets toward spherical shapes. Over time, the thickness of this elastic membrane grows, hence the bending stiffness required to change its shape eventually balances the surface stresses, which arrests the relaxation process. These results provide general rules to understand the shape of solidifying materials combining both tension and bending driven deformations.
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Affiliation(s)
- J Godefroid
- Soft Matter Science and Engineering, ESPCI Paris, PSL Research, CNRS, Sorbonne Université, 75005 Paris, France.
- Saint-Gobain Research Provence, Cavaillon, France
| | - D Bouttes
- Saint-Gobain Research Provence, Cavaillon, France
| | - A Marcellan
- Soft Matter Science and Engineering, ESPCI Paris, PSL Research, CNRS, Sorbonne Université, 75005 Paris, France.
| | - E Barthel
- Soft Matter Science and Engineering, ESPCI Paris, PSL Research, CNRS, Sorbonne Université, 75005 Paris, France.
| | - C Monteux
- Soft Matter Science and Engineering, ESPCI Paris, PSL Research, CNRS, Sorbonne Université, 75005 Paris, France.
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13
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Maji A, Dasbiswas K, Rabin Y. Shape transitions in a network model of active elastic shells. SOFT MATTER 2023; 19:7216-7226. [PMID: 37724013 DOI: 10.1039/d3sm01041d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/20/2023]
Abstract
Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex 3D shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well as hydrostatic fluid pressure, both of which are actively regulated in living matter through mechano-chemical feedback. Inspired by autonomous, biophysical shape change, such as occurring in the model organism hydra, we introduce a minimal, active, elastic model featuring a network of springs in a globe-like spherical shell geometry. In this model there is coupling between activity and the shape of the shell: if the local curvature of a filament represented by a spring falls below a critical value, its elastic constant is actively changed. This results in deformation of the springs that changes the shape of the shell. By combining excitation of springs and pressure regulation, we show that the shell undergoes a transition from spheroidal to either elongated ellipsoidal or a different spheroidal shape, depending on pressure. There exists a critical pressure at which there is an abrupt change from ellipsoids to spheroids, showing that pressure is potentially a sensitive switch for material shape. We thus offer biologically inspired design principles for autonomous shape transitions in active elastic shells.
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Affiliation(s)
- Ajoy Maji
- Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, Merced, CA 95343, USA
| | - Yitzhak Rabin
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel.
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14
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Jiang P, Zhang S, Yang H, Li Y. Suture Interface Inspired Self-Recovery Architected Structures for Reusable Energy Absorption. ACS APPLIED MATERIALS & INTERFACES 2023; 15:43102-43110. [PMID: 37561821 DOI: 10.1021/acsami.3c06463] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/12/2023]
Abstract
Designing materials and structures with high energy absorption and self-recoverability remains a challenge for reusable energy absorption, particularly in aerospace engineering applications (i.e., planetary landers). While the prevalent design methods of reusable energy absorbers mainly use the mechanical instability of tilted and curved beams, the limited energy absorption capabilities and low strength of tilted or curved beams limit performance improvement. In nature, Phlorodes diabolicus has evolved extreme impact resistance, in which the suture interface structure plays a key role. Herein, we propose a convex interface slide design strategy for reusability and energy absorption through friction interface, geometry, and bending elasticity, inspired by the elytra of Phlorodes diabolicus. Convex interfaces slide to achieve a more than 270% higher energy absorption capacity per unit volume than the curved beams. The convex interface slide design can be easily integrated with other structures to achieve multiple functions, such as various shapes and self-recoverability. Furthermore, we developed a theoretical model to predict the mechanical behavior and energy absorption performance. Our strategy opens up a new design space for creating reusable energy-absorbing structures.
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Affiliation(s)
- Peng Jiang
- State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
- Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China
| | - Shushan Zhang
- State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
- Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China
| | - Heng Yang
- State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
- Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China
| | - Ying Li
- State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
- Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China
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15
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Schulz AK, Schneider N, Zhang M, Singal K. A Year at the Forefront of Hydrostat Motion. Biol Open 2023; 12:bio059834. [PMID: 37566395 PMCID: PMC10434360 DOI: 10.1242/bio.059834] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/12/2023] Open
Abstract
Currently, in the field of interdisciplinary work in biology, there has been a significant push by the soft robotic community to understand the motion and maneuverability of hydrostats. This Review seeks to expand the muscular hydrostat hypothesis toward new structures, including plants, and introduce innovative techniques to the hydrostat community on new modeling, simulating, mimicking, and observing hydrostat motion methods. These methods range from ideas of kirigami, origami, and knitting for mimic creation to utilizing reinforcement learning for control of bio-inspired soft robotic systems. It is now being understood through modeling that different mechanisms can inhibit traditional hydrostat motion, such as skin, nostrils, or sheathed layered muscle walls. The impact of this Review will highlight these mechanisms, including asymmetries, and discuss the critical next steps toward understanding their motion and how species with hydrostat structures control such complex motions, highlighting work from January 2022 to December 2022.
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Affiliation(s)
- Andrew K. Schulz
- School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
| | - Nikole Schneider
- Department of Biology, University of South Dakota, Vermillion, SD 57069, USA
| | - Margaret Zhang
- School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
| | - Krishma Singal
- School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
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16
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Hwang D, Lee C, Yang X, Pérez-González JM, Finnegan J, Lee B, Markvicka EJ, Long R, Bartlett MD. Metamaterial adhesives for programmable adhesion through reverse crack propagation. NATURE MATERIALS 2023; 22:1030-1038. [PMID: 37349397 DOI: 10.1038/s41563-023-01577-2] [Citation(s) in RCA: 16] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 05/04/2023] [Indexed: 06/24/2023]
Abstract
Adhesives are typically either strong and permanent or reversible with limited strength. However, current strategies to create strong yet reversible adhesives needed for wearable devices, robotics and material disassembly lack independent control of strength and release, require complex fabrication or only work in specific conditions. Here we report metamaterial adhesives that simultaneously achieve strong and releasable adhesion with spatially selectable adhesion strength through programmed cut architectures. Nonlinear cuts uniquely suppress crack propagation by forcing cracks to propagate backwards for 60× enhancement in adhesion, while allowing crack growth in the opposite direction for easy release and reusability. This mechanism functions in numerous adhesives on diverse substrates in wet and dry conditions and enables highly tunable adhesion with independently programmable adhesion strength in two directions simultaneously at any location. We create these multifunctional materials in a maskless, digital fabrication framework to rapidly customize adhesive characteristics with deterministic control for next-generation adhesives.
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Affiliation(s)
- Dohgyu Hwang
- Department of Mechanical Engineering, Soft Materials and Structures Lab, Virginia Tech, Blacksburg, VA, USA
- Macromolecules Innovation Institute, Virginia Tech, Blacksburg, VA, USA
| | - Chanhong Lee
- Department of Mechanical Engineering, Soft Materials and Structures Lab, Virginia Tech, Blacksburg, VA, USA
| | - Xingwei Yang
- Department of Mechanical Engineering, University of Colorado, Boulder, CO, USA
| | | | - Jason Finnegan
- Department of Mechanical & Materials Engineering, Smart Materials and Robotics Lab, University of Nebraska-Lincoln, Lincoln, NE, USA
| | - Bernard Lee
- Department of Mechanical & Materials Engineering, Smart Materials and Robotics Lab, University of Nebraska-Lincoln, Lincoln, NE, USA
| | - Eric J Markvicka
- Department of Mechanical & Materials Engineering, Smart Materials and Robotics Lab, University of Nebraska-Lincoln, Lincoln, NE, USA
| | - Rong Long
- Department of Mechanical Engineering, University of Colorado, Boulder, CO, USA
| | - Michael D Bartlett
- Department of Mechanical Engineering, Soft Materials and Structures Lab, Virginia Tech, Blacksburg, VA, USA.
- Macromolecules Innovation Institute, Virginia Tech, Blacksburg, VA, USA.
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17
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van Kesteren S, Shen X, Aldeghi M, Isa L. Printing on Particles: Combining Two-Photon Nanolithography and Capillary Assembly to Fabricate Multimaterial Microstructures. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2207101. [PMID: 36601964 DOI: 10.1002/adma.202207101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Revised: 12/20/2022] [Indexed: 05/16/2023]
Abstract
Additive manufacturing at the micro- and nanoscale has seen a recent upsurge to suit an increasing demand for more elaborate structures. However, the integration of multiple distinct materials at small scales remains challenging. To this end, capillarity-assisted particle assembly (CAPA) and two-photon polymerization direct laser writing (2PP-DLW) are combined to realize a new class of multimaterial microstructures. 2PP-DLW and CAPA both are used to fabricate 3D templates to guide the CAPA of soft- and hard colloids, and to link well-defined arrangements of functional microparticle arrays produced by CAPA, a process that is termed "printing on particles." The printing process uses automated particle recognition algorithms to connect colloids into 1D, 2D, and 3D tailored structures, via rigid, soft, or responsive polymer links. Once printed and developed, the structures can be easily re-dispersed in water. Particle clusters and lattices of varying symmetry and composition are reported, together with thermoresponsive microactuators, and magnetically driven "micromachines", which can efficiently move, capture, and release DNA-coated particles in solution. The flexibility of this method allows the combination of a wide range of functional materials into complex structures, which will boost the realization of new systems and devices for numerous fields, including microrobotics, micromanipulation, and metamaterials.
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Affiliation(s)
- Steven van Kesteren
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 1-5/10, Zurich, 8093, Switzerland
| | - Xueting Shen
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 1-5/10, Zurich, 8093, Switzerland
| | - Michele Aldeghi
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 1-5/10, Zurich, 8093, Switzerland
| | - Lucio Isa
- Laboratory for Soft Materials and Interfaces, Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 1-5/10, Zurich, 8093, Switzerland
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18
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Analytical Solutions for a New Form of the Generalized q-Deformed Sinh–Gordon Equation: ∂2u∂z∂ζ=eαu[sinhq(uγ)]p−δ. Symmetry (Basel) 2023. [DOI: 10.3390/sym15020470] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/12/2023] Open
Abstract
In this article, a new version of the generalized q-deformed Sinh–Gordon equation is presented, and analytical solutions are developed for specific parameter sets using those equations. There is a possibility that the new equation can be used to model physical systems that have broken symmetries and include also effects related to amplification or dissipation. In addition, we have include some illustrations that depict the varied patterns of soliton propagation.
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19
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PEG-in-PDMS drops stabilised by soft silicone skins as a model system for elastocapillary emulsions with explicit morphology control. J Colloid Interface Sci 2022; 628:1044-1057. [DOI: 10.1016/j.jcis.2022.07.029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 07/01/2022] [Accepted: 07/04/2022] [Indexed: 11/19/2022]
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20
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Chi Y, Li Y, Zhao Y, Hong Y, Tang Y, Yin J. Bistable and Multistable Actuators for Soft Robots: Structures, Materials, and Functionalities. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2110384. [PMID: 35172026 DOI: 10.1002/adma.202110384] [Citation(s) in RCA: 42] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Revised: 02/04/2022] [Indexed: 06/14/2023]
Abstract
Snap-through bistability is often observed in nature (e.g., fast snapping to closure of Venus flytrap) and the life (e.g., bottle caps and hair clippers). Recently, harnessing bistability and multistability in different structures and soft materials has attracted growing interest for high-performance soft actuators and soft robots. They have demonstrated broad and unique applications in high-speed locomotion on land and under water, adaptive sensing and fast grasping, shape reconfiguration, electronics-free controls with a single input, and logic computation. Here, an overview of integrating bistable and multistable structures with soft actuating materials for diverse soft actuators and soft/flexible robots is given. The mechanics-guided structural design principles for five categories of basic bistable elements from 1D to 3D (i.e., constrained beams, curved plates, dome shells, compliant mechanisms of linkages with flexible hinges and deformable origami, and balloon structures) are first presented, alongside brief discussions of typical soft actuating materials (i.e., fluidic elastomers and stimuli-responsive materials such as electro-, photo-, thermo-, magnetic-, and hydro-responsive polymers). Following that, integrating these soft materials with each category of bistable elements for soft bistable and multistable actuators and their diverse robotic applications are discussed. To conclude, perspectives on the challenges and opportunities in this emerging field are considered.
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Affiliation(s)
- Yinding Chi
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
| | - Yanbin Li
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
| | - Yao Zhao
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
| | - Yaoye Hong
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
| | - Yichao Tang
- School of Mechanical Engineering, Tongji University, Shanghai, 200092, China
| | - Jie Yin
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, 27695, USA
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21
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Wu Y, Guo G, Wei Z, Qian J. Programming Soft Shape-Morphing Systems by Harnessing Strain Mismatch and Snap-Through Bistability: A Review. MATERIALS (BASEL, SWITZERLAND) 2022; 15:2397. [PMID: 35407728 PMCID: PMC8999758 DOI: 10.3390/ma15072397] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Revised: 03/21/2022] [Accepted: 03/22/2022] [Indexed: 02/04/2023]
Abstract
Multi-modal and controllable shape-morphing constitutes the cornerstone of the functionalization of soft actuators/robots. Involving heterogeneity through material layout is a widely used strategy to generate internal mismatches in active morphing structures. Once triggered by external stimuli, the entire structure undergoes cooperative deformation by minimizing the potential energy. However, the intrinsic limitation of soft materials emerges when it comes to applications such as soft actuators or load-bearing structures that require fast response and large output force. Many researchers have explored the use of the structural principle of snap-through bistability as the morphing mechanisms. Bistable or multi-stable mechanical systems possess more than one local energy minimum and are capable of resting in any of these equilibrium states without external forces. The snap-through motion could overcome energy barriers to switch among these stable or metastable states with dramatically distinct geometries. Attributed to the energy storage and release mechanism, such snap-through transition is quite highly efficient, accompanied by fast response speed, large displacement magnitude, high manipulation strength, and moderate driving force. For example, the shape-morphing timescale of conventional hydrogel systems is usually tens of minutes, while the activation time of hydrogel actuators using the elastic snapping instability strategy can be reduced to below 1 s. By rationally embedding stimuli-responsive inclusions to offer the required trigger energy, various controllable snap-through actuations could be achieved. This review summarizes the current shape-morphing programming strategies based on mismatch strain induced by material heterogeneity, with emphasis on how to leverage snap-through bistability to broaden the applications of the shape-morphing structures in soft robotics and mechanical metamaterials.
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Affiliation(s)
| | | | | | - Jin Qian
- Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China; (Y.W.); (G.G.); (Z.W.)
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22
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Jouanlanne M, Egelé A, Favier D, Drenckhan W, Farago J, Hourlier-Fargette A. Elastocapillary deformation of thin elastic ribbons in 2D foam columns. SOFT MATTER 2022; 18:2325-2331. [PMID: 35174372 PMCID: PMC9466004 DOI: 10.1039/d1sm01687c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/27/2021] [Accepted: 01/29/2022] [Indexed: 06/14/2023]
Abstract
The ability of liquid interfaces to shape slender elastic structures provides powerful strategies to control the architecture of mechanical self assemblies. However, elastocapillarity-driven intelligent design remains unexplored in more complex architected liquids - such as foams. Here we propose a model system which combines an assembly of bubbles and a slender elastic structure. Arrangements of soap bubbles in confined environments form well-defined periodic structures, dictated by Plateau's laws. We consider a 2D foam column formed in a container with square cross-section in which we introduce an elastomer ribbon, leading to architected structures whose geometry is guided by a competition between elasticity and capillarity. In this system, we quantify both experimentally and theoretically the equilibrium shapes, using X-ray micro-tomography and energy minimisation techniques. Beyond the understanding of the amplitude of the wavy elastic ribbon deformation, we provide a detailed analysis of the profile of the ribbon, and show that such a setup can be used to grant a shape to a UV-curable composite slender structure, as a foam-forming technique suitable to miniaturisation. In more general terms, this work provides a stepping stone towards an improved understanding of the interactions between liquid foams and slender structures.
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Affiliation(s)
- Manon Jouanlanne
- Université de Strasbourg, CNRS, Institut Charles Sadron UPR22, F-67000 Strasbourg, France.
| | - Antoine Egelé
- Université de Strasbourg, CNRS, Institut Charles Sadron UPR22, F-67000 Strasbourg, France.
| | - Damien Favier
- Université de Strasbourg, CNRS, Institut Charles Sadron UPR22, F-67000 Strasbourg, France.
| | - Wiebke Drenckhan
- Université de Strasbourg, CNRS, Institut Charles Sadron UPR22, F-67000 Strasbourg, France.
| | - Jean Farago
- Université de Strasbourg, CNRS, Institut Charles Sadron UPR22, F-67000 Strasbourg, France.
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23
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Hwang D, Barron EJ, Haque ABMT, Bartlett MD. Shape morphing mechanical metamaterials through reversible plasticity. Sci Robot 2022; 7:eabg2171. [PMID: 35138882 DOI: 10.1126/scirobotics.abg2171] [Citation(s) in RCA: 33] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Biological organisms such as the octopus can reconfigure their shape and properties to perform diverse tasks. However, soft machines struggle to achieve complex configurations, morph into shape to support loads, and go between multiple states reversibly. Here, we introduce a multifunctional shape-morphing material with reversible and rapid polymorphic reconfigurability. We couple elastomeric kirigami with an unconventional reversible plasticity mechanism in metal alloys to rapidly (<0.1 seconds) morph flat sheets into complex, load-bearing shapes, with reversibility and self-healing through phase change. This kirigami composite overcomes trade-offs in deformability and load-bearing capacity and eliminates power requirements to sustain reconfigured shapes. We demonstrate this material through integration with onboard control, motors, and power to create a soft robotic morphing drone, which autonomously transforms from a ground to air vehicle and an underwater morphing machine, which can be reversibly deployed to collect cargo.
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Affiliation(s)
- Dohgyu Hwang
- Macromolecules Innovation Institute, Virginia Tech, Blacksburg, VA 24061, USA.,Department of Mechanical Engineering, Soft Materials and Structures Lab, Virginia Tech, Blacksburg, VA 24061, USA
| | - Edward J Barron
- Macromolecules Innovation Institute, Virginia Tech, Blacksburg, VA 24061, USA.,Department of Mechanical Engineering, Soft Materials and Structures Lab, Virginia Tech, Blacksburg, VA 24061, USA
| | - A B M Tahidul Haque
- Department of Mechanical Engineering, Soft Materials and Structures Lab, Virginia Tech, Blacksburg, VA 24061, USA
| | - Michael D Bartlett
- Macromolecules Innovation Institute, Virginia Tech, Blacksburg, VA 24061, USA.,Department of Mechanical Engineering, Soft Materials and Structures Lab, Virginia Tech, Blacksburg, VA 24061, USA
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24
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Stein-Montalvo L, Lee JH, Yang Y, Landesberg M, Park HS, Holmes DP. Efficient snap-through of spherical caps by applying a localized curvature stimulus. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:3. [PMID: 35024982 DOI: 10.1140/epje/s10189-021-00156-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Accepted: 12/16/2021] [Indexed: 06/14/2023]
Abstract
In bistable actuators and other engineered devices, a homogeneous stimulus (e.g., mechanical, chemical, thermal, or magnetic) is often applied to an entire shell to initiate a snap-through instability. In this work, we demonstrate that restricting the active area to the shell boundary allows for a large reduction in its size, thereby decreasing the energy input required to actuate the shell. To do so, we combine theory with 1D finite element simulations of spherical caps with a non-homogeneous distribution of stimulus-responsive material. We rely on the effective curvature stimulus, i.e., the natural curvature induced by the non-mechanical stimulus, which ensures that our results are entirely stimulus-agnostic. To validate our numerics and demonstrate this generality, we also perform two sets of experiments, wherein we use residual swelling of bilayer silicone elastomers-a process that mimics differential growth-as well as a magneto-elastomer to induce curvatures that cause snap-through. Our results elucidate the underlying mechanics, offering an intuitive route to optimal design for efficient snap-through.
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Affiliation(s)
- Lucia Stein-Montalvo
- Department of Mechanical Engineering, Boston University, Boston, USA
- Department of Civil and Environmental Engineering, Princeton University, Princeton, USA
| | - Jeong-Ho Lee
- Department of Mechanical Engineering, Boston University, Boston, USA
| | - Yi Yang
- Department of Mechanical Engineering, Boston University, Boston, USA
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, USA
| | - Melanie Landesberg
- Department of Mechanical Engineering, Boston University, Boston, USA
- Yale University, New Haven, USA
| | - Harold S Park
- Department of Mechanical Engineering, Boston University, Boston, USA
| | - Douglas P Holmes
- Department of Mechanical Engineering, Boston University, Boston, USA.
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25
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Oshri O. Asymptotic softness of a laterally confined sheet in a pressurized chamber. Phys Rev E 2021; 104:055005. [PMID: 34942726 DOI: 10.1103/physreve.104.055005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2021] [Accepted: 10/18/2021] [Indexed: 11/07/2022]
Abstract
Elastohydrodynamic models, that describe the interaction between a thin sheet and a fluid medium, have been proven successful in explaining the complex behavior of biological systems and artificial materials. Motivated by these applications we study the quasistatic deformation of a thin sheet that is confined between the two sides of a closed chamber. The two parts of the chamber, above and below the sheet, are filled with an ideal gas. We show that the system is governed by two dimensionless parameters, Δ and η, that account respectively for the lateral compression of the sheet and the ratio between the amount of fluid filling each part of the chamber and the bending stiffness of the sheet. When η≪1 the bending energy of the sheet dominates the system, the pressure drop between the two sides of the chamber increases, and the sheet exhibits a symmetric configuration. When η≫1 the energy of the fluid dominates the system, the pressure drop vanishes, and the sheet exhibits an asymmetric configuration. The transition between these two limiting scenarios is governed by a third branch of solutions that is characterized by a rapid decrease of the pressure drop. Notably, across the transition the energetic gap between the symmetric and asymmetric states scales as δE∼Δ^{2}. Therefore, in the limit Δ≪1 small variations in the energy are accompanied by relatively large changes in the elastic shape.
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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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26
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Stein-Montalvo L, Holmes DP, Coupier G. Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0253] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures, i.e. below the experimentally determined critical load at which buckling occurs elastically, often following a significant delay period from the time of load application. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centred on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the deflection at instability and the time delay depend on the applied pressure, material properties and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behaviour from an elastic shell buckling perspective but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.
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Affiliation(s)
| | - Douglas P. Holmes
- Department of Mechanical Engineering, Boston University, Boston, MA, USA
| | - Gwennou Coupier
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, Saint-Martin-d’Heres, France
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27
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Mokbel M, Djellouli A, Quilliet C, Aland S, Coupier G. Post-buckling dynamics of spherical shells. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0378] [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
We explore the intrinsic dynamics of spherical shells immersed in a fluid in the vicinity of their buckled state, through experiments and three-dimensional axisymmetric simulations. The results are supported by a theoretical model that accurately describes the buckled shell as a two-variable-only oscillator. We quantify the effective ‘softening’ of shells above the buckling threshold, as observed in recent experiments on interactions between encapsulated microbubbles and acoustic waves. The main dissipation mechanism in the neighbouring fluid is also evidenced.
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Affiliation(s)
- Marcel Mokbel
- University of Applied Sciences (HTW) Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany
- Technische Universität Bergakademie Freiberg, Akademiestrasse,609599 Freiberg, Germany
| | - Adel Djellouli
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
- School of Engineering and Applied Sciences Cambridge, Harvard University, Cambridge, MA 02138, USA
| | | | - Sebastian Aland
- University of Applied Sciences (HTW) Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany
- Technische Universität Bergakademie Freiberg, Akademiestrasse,609599 Freiberg, Germany
| | - Gwennou Coupier
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
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28
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Sharma M, Jiang T, Jiang ZC, Moguel-Lehmer CE, Harris TJ. Emergence of a smooth interface from growth of a dendritic network against a mechanosensitive contractile material. eLife 2021; 10:66929. [PMID: 34423780 PMCID: PMC8410080 DOI: 10.7554/elife.66929] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 08/20/2021] [Indexed: 11/13/2022] Open
Abstract
Structures and machines require smoothening of raw materials. Self-organized smoothening guides cell and tissue morphogenesis and is relevant to advanced manufacturing. Across the syncytial Drosophila embryo surface, smooth interfaces form between expanding Arp2/3-based actin caps and surrounding actomyosin networks, demarcating the circumferences of nascent dome-like compartments used for pseudocleavage. We found that forming a smooth and circular boundary of the surrounding actomyosin domain requires Arp2/3 in vivo. To dissect the physical basis of this requirement, we reconstituted the interacting networks using node-based models. In simulations of actomyosin networks with local clearances in place of Arp2/3 domains, rough boundaries persisted when myosin contractility was low. With addition of expanding Arp2/3 network domains, myosin domain boundaries failed to smoothen, but accumulated myosin nodes and tension. After incorporating actomyosin mechanosensitivity, Arp2/3 network growth locally induced a surrounding contractile actomyosin ring that smoothened the interface between the cytoskeletal domains, an effect also evident in vivo. In this way, a smooth structure can emerge from the lateral interaction of irregular active materials.
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Affiliation(s)
- Medha Sharma
- Department of Cell and Systems Biology, University of Toronto, Toronto, Canada
| | - Tao Jiang
- Department of Cell and Systems Biology, University of Toronto, Toronto, Canada
| | - Zi Chen Jiang
- Department of Cell and Systems Biology, University of Toronto, Toronto, Canada
| | | | - Tony Jc Harris
- Department of Cell and Systems Biology, University of Toronto, Toronto, Canada
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29
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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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30
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Zakharov A, Dasbiswas K. Modeling mechanochemical pattern formation in elastic sheets of biological matter. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:82. [PMID: 34159454 DOI: 10.1140/epje/s10189-021-00086-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
Inspired by active shape morphing in developing tissues and biomaterials, we investigate two generic mechanochemical models where the deformations of a thin elastic sheet are driven by, and in turn affect, the concentration gradients of a chemical signal. We develop numerical methods to study the coupled elastic deformations and chemical concentration kinetics, and illustrate with computations the formation of different patterns depending on shell thickness, strength of mechanochemical coupling and diffusivity. In the first model, the sheet curvature governs the production of a contractility inhibitor and depending on the threshold in the coupling, qualitatively different patterns occur. The second model is based on the stress-dependent activity of myosin motors and demonstrates how the concentration distribution patterns of molecular motors are affected by the long-range deformations generated by them. Since the propagation of mechanical deformations is typically faster than chemical kinetics (of molecular motors or signaling agents that affect motors), we describe in detail and implement a numerical method based on separation of timescales to effectively simulate such systems. We show that mechanochemical coupling leads to long-range propagation of patterns in disparate systems through elastic instabilities even without the diffusive or advective transport of the chemicals.
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Affiliation(s)
- Andrei Zakharov
- Department of Physics, University of California, Merced, CA, 95343, USA
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, CA, 95343, USA.
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31
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Yang Y, Vella K, Holmes DP. Grasping with kirigami shells. Sci Robot 2021; 6:6/54/eabd6426. [PMID: 34043535 DOI: 10.1126/scirobotics.abd6426] [Citation(s) in RCA: 38] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Accepted: 04/19/2021] [Indexed: 12/13/2022]
Abstract
The ability to grab, hold, and manipulate objects is a vital and fundamental operation in biological and engineering systems. Here, we present a soft gripper using a simple material system that enables precise and rapid grasping, and can be miniaturized, modularized, and remotely actuated. This soft gripper is based on kirigami shells-thin, elastic shells patterned with an array of cuts. The kirigami cut pattern is determined by evaluating the shell's mechanics and geometry, using a combination of experiments, finite element simulations, and theoretical modeling, which enables the gripper design to be both scalable and material independent. We demonstrate that the kirigami shell gripper can be readily integrated with an existing robotic platform or remotely actuated using a magnetic field. The kirigami cut pattern results in a simple unit cell that can be connected together in series, and again in parallel, to create kirigami gripper arrays capable of simultaneously grasping multiple delicate and slippery objects. These soft and lightweight grippers will have applications in robotics, haptics, and biomedical device design.
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Affiliation(s)
- Yi Yang
- Department of Mechanical Engineering, Boston University, 110 Cummington Mall, Boston, MA 02215, USA
| | - Katherine Vella
- Department of Mechanical Engineering, Boston University, 110 Cummington Mall, Boston, MA 02215, USA
| | - Douglas P Holmes
- Department of Mechanical Engineering, Boston University, 110 Cummington Mall, Boston, MA 02215, USA
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32
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Zakharov A, Dasbiswas K. Mechanochemical induction of wrinkling morphogenesis on elastic shells. SOFT MATTER 2021; 17:4738-4750. [PMID: 33978668 DOI: 10.1039/d1sm00003a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that cell shape changes are induced by diffusible biomolecules that influence tissue contractility in a concentration-dependent manner - and whose concentration is in turn affected by the macroscopic tissue shape. We perform computational simulations of thin shell elastic dynamics to reveal propagating chemical and three-dimensional deformation patterns arising due to a sequence of buckling instabilities. Depending on the concentration threshold that actuates cell shape change, we find qualitatively different patterns. The mechanochemically coupled patterning dynamics are distinct from those driven by purely mechanical or purely chemical factors, and emerge even without diffusion. Using numerical simulations and theoretical arguments, we analyze the elastic instabilities that result from our model and provide simple scaling laws to identify wrinkling morphologies.
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Affiliation(s)
- Andrei Zakharov
- Department of Physics, University of California, Merced, Merced, CA 95343, USA.
| | - Kinjal Dasbiswas
- Department of Physics, University of California, Merced, Merced, CA 95343, USA.
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33
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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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34
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Davidovitch B, Démery V. Rucks and folds: delamination from a flat rigid substrate under uniaxial compression. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:11. [PMID: 33683490 DOI: 10.1140/epje/s10189-021-00020-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 01/15/2021] [Indexed: 06/12/2023]
Abstract
We revisit the delamination of a solid adhesive sheet under uniaxial compression from a flat, rigid substrate. Using energetic considerations and scaling arguments, we show that the phenomenology is governed by three dimensionless groups, which characterize the level of confinement imposed on the sheet, as well as its extensibility and bendability. Recognizing that delamination emerges through a subcritical bifurcation from a planar, uniformly compressed state, we predict that the dependence of the threshold confinement level on the extensibility and bendability of the sheet, as well as the delaminated shape at threshold, varies markedly between two asymptotic regimes of these parameters. For sheets whose bendability is sufficiently high, the delaminated shape is a large-slope "fold," where the amplitude is proportional to the imposed confinement. In contrast, for lower values of the bendability parameter, the delaminated shape is a small-slope "ruck," whose amplitude increases more moderately upon increasing confinement. Realizing that the instability of the fully laminated state requires a finite extensibility of the sheet, we introduce a simple model that allows us to construct a bifurcation diagram that governs the delamination process.
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Affiliation(s)
- Benny Davidovitch
- Department of Physics, University of Massachusetts Amherst, Amherst, MA, 01003, USA
| | - Vincent Démery
- Gulliver, CNRS, ESPCI Paris PSL, 10 rue Vauquelin, 75005, Paris, France.
- Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, 69342, Lyon, France.
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35
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Yoshida K, Wada H. Mechanics of a Snap Fit. PHYSICAL REVIEW LETTERS 2020; 125:194301. [PMID: 33216583 DOI: 10.1103/physrevlett.125.194301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Accepted: 09/28/2020] [Indexed: 06/11/2023]
Abstract
Snap fits are versatile mechanical designs in industrial products that enable the repeated assembling and disassembling of two solid parts. This important property is attributed to a fine balance between geometry, friction, and bending elasticity. In this Letter, we combine theory, simulation, and experiment to reveal the fundamental physical principles of snap-fit functions in the simplest possible setup consisting of a rigid cylinder and a thin elastic shell. We construct a phase diagram using geometric parameters and identify four distinct mechanical phases. We develop analytical predictions based on the linear elasticity theory combined with the law of static friction and rationalize the numerical and experimental results. The study reveals how an operational asymmetry of snap fits (i.e., easy to assemble but difficult to disassemble) emerges from an exquisite combination of geometry, elasticity, and friction and suggests optimization of the tunable functionalities for a range of mechanical designs.
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Affiliation(s)
- Keisuke Yoshida
- Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
| | - Hirofumi Wada
- Department of Physical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
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36
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Plummer A, Nelson DR. Buckling and metastability in membranes with dilation arrays. Phys Rev E 2020; 102:033002. [PMID: 33075876 DOI: 10.1103/physreve.102.033002] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 07/07/2020] [Indexed: 11/07/2022]
Abstract
We study periodic arrays of impurities that create localized regions of expansion, embedded in two-dimensional crystalline membranes. These arrays provide a simple elastic model of shape memory. As the size of each dilational impurity increases (or the relative cost of bending to stretching decreases), it becomes energetically favorable for each of the M impurities to buckle up or down into the third dimension, thus allowing for of order 2^{M} metastable surface configurations corresponding to different impurity "spin" configurations. With both discrete simulations and the nonlinear continuum theory of elastic plates, we explore the buckling of both isolated dilations and dilation arrays at zero temperature, guided by analogies with Ising antiferromagnets. We conjecture ground states for systems with triangular and square impurity superlattices, and comment briefly on the possible behaviors at finite temperatures.
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Affiliation(s)
- Abigail Plummer
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - David R Nelson
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
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37
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Oratis AT, Bush JWM, Stone HA, Bird JC. A new wrinkle on liquid sheets: Turning the mechanism of viscous bubble collapse upside down. Science 2020; 369:685-688. [PMID: 32764069 DOI: 10.1126/science.aba0593] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2019] [Accepted: 06/25/2020] [Indexed: 11/02/2022]
Abstract
Viscous bubbles are prevalent in both natural and industrial settings. Their rupture and collapse may be accompanied by features typically associated with elastic sheets, including the development of radial wrinkles. Previous investigators concluded that the film weight is responsible for both the film collapse and wrinkling instability. Conversely, we show here experimentally that gravity plays a negligible role: The same collapse and wrinkling arise independently of the bubble's orientation. We found that surface tension drives the collapse and initiates a dynamic buckling instability. Because the film weight is irrelevant, our results suggest that wrinkling may likewise accompany the breakup of relatively small-scale, curved viscous and viscoelastic films, including those in the respiratory tract responsible for aerosol production from exhalation events.
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Affiliation(s)
- Alexandros T Oratis
- Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA
| | - John W M Bush
- Department of Applied Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Howard A Stone
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
| | - James C Bird
- Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA.
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38
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Holmes DP, Lee JH, Park HS, Pezzulla M. Nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature. Phys Rev E 2020; 102:023003. [PMID: 32942434 DOI: 10.1103/physreve.102.023003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 07/22/2020] [Indexed: 11/07/2022]
Abstract
In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Nonmechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prevalent in a wide range of natural and engineered systems, and may occur due to thermal expansion, changes in pH, differential swelling, and differential growth. Here we investigate how the presence of both an evolving natural curvature and an external pressure modifies the stability of a complete spherical shell. We show that due to a mechanical analogy between pressure and curvature, positive natural curvatures can severely destabilize a thin shell, while negative natural curvatures can strengthen the shell against buckling, providing the possibility to design shells that buckle at or above the theoretical limit for pressure alone, i.e., a strengthening factor. These results extend directly from the classical analysis of the stability of shells under pressure, and highlight the important role that nonmechanical stimuli can have on modifying the membrane state of stress in a thin shell.
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Affiliation(s)
- Douglas P Holmes
- Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA
| | - Jeong-Ho Lee
- Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA
| | - Harold S Park
- Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA
| | - Matteo Pezzulla
- Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
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39
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Liu M, Domino L, Vella D. Tapered elasticæ as a route for axisymmetric morphing structures. SOFT MATTER 2020; 16:7739-7750. [PMID: 32743628 DOI: 10.1039/d0sm00714e] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Transforming flat two-dimensional (2D) sheets into three-dimensional (3D) structures by combining carefully made cuts with applied edge-loads has emerged as an exciting manufacturing paradigm in a range of applications from mechanical metamaterials to flexible electronics. In Kirigami, patterns of cuts are introduced that allow solid faces to rotate about each other, deforming in three dimensions whilst remaining planar. In other scenarios, however, the solid elements bend in one direction. In this paper, we model such bending deformations using the formulation of an elastic strip whose thickness and width are tapered (the 'tapered elastica'). We show how this framework can be exploited to design the tapering patterns required to create planar sheets that morph into desired axisymmetric 3D shapes under a combination of horizontal and vertical edge-loads. We exhibit this technique by recreating miniature structures with positive, negative, and variable apparent Gaussian curvatures. With sheets of constant thickness, the resulting morphed shapes may leave gaps between the deformed elements. However, by tapering the thickness of the sheet too, these gaps can be closed, creating tessellated three-dimensional structures. Our theoretical approaches are verified by both numerical simulations and physical experiments.
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Affiliation(s)
- Mingchao Liu
- Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
| | - Lucie Domino
- Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
| | - Dominic Vella
- Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
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40
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Bonfanti S, Guerra R, Font-Clos F, Rayneau-Kirkhope D, Zapperi S. Automatic design of mechanical metamaterial actuators. Nat Commun 2020; 11:4162. [PMID: 32820158 PMCID: PMC7441157 DOI: 10.1038/s41467-020-17947-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Accepted: 07/23/2020] [Indexed: 02/06/2023] Open
Abstract
Mechanical metamaterial actuators achieve pre-determined input–output operations exploiting architectural features encoded within a single 3D printed element, thus removing the need for assembling different structural components. Despite the rapid progress in the field, there is still a need for efficient strategies to optimize metamaterial design for a variety of functions. We present a computational method for the automatic design of mechanical metamaterial actuators that combines a reinforced Monte Carlo method with discrete element simulations. 3D printing of selected mechanical metamaterial actuators shows that the machine-generated structures can reach high efficiency, exceeding human-designed structures. We also show that it is possible to design efficient actuators by training a deep neural network which is then able to predict the efficiency from the image of a structure and to identify its functional regions. The elementary actuators devised here can be combined to produce metamaterial machines of arbitrary complexity for countless engineering applications. Efficient strategies to optimize metamaterial design for specific applications are urgently needed despite the rapid progress in this area. Here the authors propose a computational method combining an optimization algorithm with discrete element simulations for the automatic design of mechanical metamaterial actuators.
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Affiliation(s)
- Silvia Bonfanti
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, Milano, 20133, Italy
| | - Roberto Guerra
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, Milano, 20133, Italy
| | - Francesc Font-Clos
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, Milano, 20133, Italy
| | - Daniel Rayneau-Kirkhope
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, Milano, 20133, Italy
| | - Stefano Zapperi
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, Milano, 20133, Italy. .,CNR - Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l'Energia, Via R. Cozzi 53, Milano, 20125, Italy.
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41
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Deng B, Chen L, Wei D, Tournat V, Bertoldi K. Pulse-driven robot: Motion via solitary waves. SCIENCE ADVANCES 2020; 6:eaaz1166. [PMID: 32494671 PMCID: PMC7195187 DOI: 10.1126/sciadv.aaz1166] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 01/17/2020] [Indexed: 06/11/2023]
Abstract
The unique properties of nonlinear waves have been recently exploited to enable a wide range of applications, including impact mitigation, asymmetric transmission, switching, and focusing. Here, we demonstrate that the propagation of nonlinear waves can be as well harnessed to make flexible structures crawl. By combining experimental and theoretical methods, we show that such pulse-driven locomotion reaches a maximum efficiency when the initiated pulses are solitons and that our simple machine can move on a wide range of surfaces and even steer. Our study expands the range of possible applications of nonlinear waves and demonstrates that they offer a new platform to make flexible machines to move.
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Affiliation(s)
- Bolei Deng
- Harvard John A. Paulson School of Engineering and Applied Sciences Harvard University, Cambridge, MA 02138, USA
| | - Liyuan Chen
- Harvard John A. Paulson School of Engineering and Applied Sciences Harvard University, Cambridge, MA 02138, USA
| | - Donglai Wei
- LAUM, CNRS, Le Mans Université, Av. O. Messiaen, 72085 Le Mans, France
| | - Vincent Tournat
- Kavli Institute, Harvard University, Cambridge, MA 02138, USA
| | - Katia Bertoldi
- Harvard John A. Paulson School of Engineering and Applied Sciences Harvard University, Cambridge, MA 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Cambridge, MA 02138, USA
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42
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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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43
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Fallahi H, Zhang J, Phan HP, Nguyen NT. Flexible Microfluidics: Fundamentals, Recent Developments, and Applications. MICROMACHINES 2019; 10:E830. [PMID: 31795397 PMCID: PMC6953028 DOI: 10.3390/mi10120830] [Citation(s) in RCA: 75] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 11/26/2019] [Accepted: 11/26/2019] [Indexed: 12/20/2022]
Abstract
Miniaturization has been the driving force of scientific and technological advances over recent decades. Recently, flexibility has gained significant interest, particularly in miniaturization approaches for biomedical devices, wearable sensing technologies, and drug delivery. Flexible microfluidics is an emerging area that impacts upon a range of research areas including chemistry, electronics, biology, and medicine. Various materials with flexibility and stretchability have been used in flexible microfluidics. Flexible microchannels allow for strong fluid-structure interactions. Thus, they behave in a different way from rigid microchannels with fluid passing through them. This unique behaviour introduces new characteristics that can be deployed in microfluidic applications and functions such as valving, pumping, mixing, and separation. To date, a specialised review of flexible microfluidics that considers both the fundamentals and applications is missing in the literature. This review aims to provide a comprehensive summary including: (i) Materials used for fabrication of flexible microfluidics, (ii) basics and roles of flexibility on microfluidic functions, (iii) applications of flexible microfluidics in wearable electronics and biology, and (iv) future perspectives of flexible microfluidics. The review provides researchers and engineers with an extensive and updated understanding of the principles and applications of flexible microfluidics.
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Affiliation(s)
| | | | | | - Nam-Trung Nguyen
- Queensland Micro and Nanotechnology Centre, Griffith University, Brisbane, QLD 4111, Australia; (H.F.); (J.Z.); (H.-P.P.)
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44
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Coupier G, Djellouli A, Quilliet C. Let's deflate that beach ball. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:129. [PMID: 31571019 DOI: 10.1140/epje/i2019-11900-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Accepted: 08/27/2019] [Indexed: 06/10/2023]
Abstract
We investigate the relationship between pre-buckling and post-buckling states as a function of shell properties, within the deflation process of shells of an isotropic material. With an original and low-cost set-up that allows to measure simultaneously volume and pressure, elastic shells whose relative thicknesses span on a broad range are deflated until they buckle. We characterize the post-buckling state in the pressure-volume diagram, but also the relaxation toward this state. The main result is that before as well as after the buckling, the shells behave in a way compatible with predictions generated through thin shell assumption, and that this consistency persists for shells where the thickness reaches up to 0.3 the shell's midsurface radius.
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Affiliation(s)
| | - Adel Djellouli
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000, Grenoble, France
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45
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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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46
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47
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Editorial overview: Particle system shape change and response. Curr Opin Colloid Interface Sci 2019. [DOI: 10.1016/j.cocis.2019.03.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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