1
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Tanaka M, Song Y, Nomura T. Fabric soft pneumatic actuators with programmable turing pattern textures. Sci Rep 2024; 14:19175. [PMID: 39160199 PMCID: PMC11333703 DOI: 10.1038/s41598-024-69450-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Accepted: 08/05/2024] [Indexed: 08/21/2024] Open
Abstract
This paper presents a novel computational design and fabrication method for fabric-based soft pneumatic actuators (FSPAs) that use Turing patterns, inspired by Alan Turing's morphogenesis theory. These inflatable structures can adapt their shapes with simple pressure changes and are applicable in areas like soft robotics, airbags, and temporary shelters. Traditionally, the design of such structures relies on isotropic materials and the designer's expertise, often requiring a trial-and-error approach. The present study introduces a method to automate this process using advanced numerical optimization to design and manufacture fabric-based inflatable structures with programmable shape-morphing capabilities. Initially, an optimized distribution of the material orientation field on the surface membrane is achieved through gradient-based orientation optimization. This involves a comprehensive physical deployment simulation using the nonlinear shell finite element method, which is integrated into the inner loop of the optimization algorithm. This continuous adjustment of material orientations enhances the design objectives. These material orientation fields are transformed into discretized texture patterns that replicate the same anisotropic deformations. Anisotropic reaction-diffusion equations, using diffusion coefficients determined by local orientations from the optimization step, are then utilized to create space-filling Turing pattern textures. Furthermore, the fabrication methods of these optimized Turing pattern textures are explored using fabrics through heat bonding and embroidery. The performance of the fabricated FSPAs is evaluated through three different deformation shapes: C-shaped bending, S-shaped bending, and twisting.
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Affiliation(s)
- Masato Tanaka
- Toyota Central R&D Laboratories, Inc., 41-1, Yokomichi, Nagakute, Aichi, 480-1192, Japan.
- Toyota Research Institute of North America, Toyota Motor North America, Ann Arbor, MI, 48105, USA.
| | - Yuyang Song
- Toyota Research Institute of North America, Toyota Motor North America, Ann Arbor, MI, 48105, USA.
| | - Tsuyoshi Nomura
- Toyota Central R&D Laboratories, Inc., 41-1, Yokomichi, Nagakute, Aichi, 480-1192, Japan
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2
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Yang X, Chen Y, Chen T, Li J, Wang Y. Active Fabrics With Controllable Stiffness for Robotic Assistive Interfaces. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2404502. [PMID: 38822632 DOI: 10.1002/adma.202404502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2024] [Revised: 05/27/2024] [Indexed: 06/03/2024]
Abstract
Assistive interfaces enable collaborative interactions between humans and robots. In contrast to traditional rigid devices, conformable fabrics with tunable mechanical properties have emerged as compelling alternatives. However, existing assistive fabrics actuated by fluidic or thermal stimuli struggle to adapt to complex body contours and are hindered by challenges such as large volumes after actuation and slow response rates. To overcome these limitations, inspiration is drawn from biological protective organisms combining hard and soft phases, and active assistive fabrics consisting of architectured rigid tiles interconnected with flexible actuated fibers are proposed. Through programmable tessellation of target body shapes into architectured tiles and controlling their interactions by the actuated fibers, the active fabrics can rapidly transition between soft compliant configurations and rigid states conformable to the body (>350 times stiffness change) while minimizing the device volume after actuation. The versatility of these active fabrics is demonstrated as exosuits for tremor suppression and lifting assistance, as body armors for impact mitigation, and integration with electrothermal actuators for smart actuation with convenient folding capabilities. This work offers a practical framework for designing customizable active fabrics with shape adaptivity and controllable stiffness, suitable for applications in wearable exosuits, haptic devices, and medical rehabilitation systems.
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Affiliation(s)
- Xudong Yang
- School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, 639798, Singapore
| | - Yu Chen
- School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, 639798, Singapore
| | - Tianyu Chen
- School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, 639798, Singapore
| | - Junwei Li
- School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, 639798, Singapore
| | - Yifan Wang
- School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, 639798, Singapore
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3
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Cheng W, Zhang W, Tao J, Zheng F, Chu B, Wang R, Fang C, Huai L, Tao P, Song C, Shang W, Fu B, Deng T. Octopus-like Microstructure of Graphene Oxide Generated through Laser-Microdroplet Interaction for Adhesive Coating. ACS NANO 2024; 18:7877-7889. [PMID: 38450636 DOI: 10.1021/acsnano.3c08635] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/08/2024]
Abstract
The octopus, as one of the most famous celebrities in bionics, has provided various inspirations for camouflage materials, soft-bodied robots, and flexible grabbers. The miniaturization of such structures will help the development of microrobots, microdelivery of drugs, and surface coating. With the lack of relevant effective preparation approaches, however, the generation of such octopus-like structures with a size of ∼1 μm or below is challenging. Here, we develop an approach based on laser-microdroplet interaction for generating an octopus-like structure with a size of ∼1 μm. The developed approach uses laser-microdroplet interaction to provide a large driving force of ∼107 Pa at a confined space (<1 μm), locally crumpling the precursor in the microdroplet. The locally crumpled particles possess both crumpled and uncrumpled structures that resemble an octopus's head and soft body. In the adhesion test, the octopus-like particles exhibit high adhesive properties in air, in water, and on a flexible substrate. In the electrochemical test, the octopus-like particles on flexible electrodes show good electrochemical and adhesive properties under hundreds of bending cycles. Benefiting from the combination of crumpled and uncrumpled morphologies, the created particles with octopus-like microstructure are demonstrated to possess comprehensive performance, exhibiting wide application potentials in the fields of microswimmers, surface coatings, and electrochemistry. Additionally, the method developed in this work has the advantages of concentrated energy in a confined space, displaying prospective potentials in micro- and nanoprocessing.
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Affiliation(s)
- Weizheng Cheng
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Wanli Zhang
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Jinran Tao
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Feiyu Zheng
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Ben Chu
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Ruitong Wang
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Cheng Fang
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Lei Huai
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Peng Tao
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Chengyi Song
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Wen Shang
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Benwei Fu
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Tao Deng
- State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
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Meeussen AS, van Hecke M. Multistable sheets with rewritable patterns for switchable shape-morphing. Nature 2023; 621:516-520. [PMID: 37730868 DOI: 10.1038/s41586-023-06353-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 06/21/2023] [Indexed: 09/22/2023]
Abstract
Flat sheets patterned with folds, cuts or swelling regions can deform into complex three-dimensional shapes under external stimuli1-24. However, current strategies require prepatterning and lack intrinsic shape selection5-24. Moreover, they either rely on permanent deformations6,12-14,17,18, preventing corrections or erasure of a shape, or sustained stimulation5,7-11,25, thus yielding shapes that are unstable. Here we show that shape-morphing strategies based on mechanical multistability can overcome these limitations. We focus on undulating metasheets that store memories of mechanical stimuli in patterns of self-stabilizing scars. After removing external stimuli, scars persist and force the sheet to switch to sharply selected curved, curled and twisted shapes. These stable shapes can be erased by appropriate forcing, allowing rewritable patterns and repeated and robust actuation. Our strategy is material agnostic, extendable to other undulation patterns and instabilities, and scale-free, allowing applications from miniature to architectural scales.
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Affiliation(s)
- A S Meeussen
- AMOLF, Amsterdam, the Netherlands.
- Huygens-Kamerlingh Onnes Laboratory, Universiteit Leiden, Leiden, the Netherlands.
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
| | - M van Hecke
- AMOLF, Amsterdam, the Netherlands
- Huygens-Kamerlingh Onnes Laboratory, Universiteit Leiden, Leiden, the Netherlands
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5
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He M, Démery V, Paulsen JD. Cross-sections of doubly curved sheets as confined elastica. Proc Natl Acad Sci U S A 2023; 120:e2216786120. [PMID: 36897985 PMCID: PMC10089198 DOI: 10.1073/pnas.2216786120] [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: 10/01/2022] [Accepted: 01/28/2023] [Indexed: 03/12/2023] Open
Abstract
Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional (3D) shapes, producing a plethora of structures across multiple length scales. To understand this complex response, previous studies have either focused on the overall gross shape or the small-scale buckling that decorates it. A geometric model, which considers the sheet as inextensible yet free to compress, has been shown to capture the gross shape of the sheet. However, the precise meaning of such predictions, and how the gross shape constrains the fine features, remains unclear. Here, we study a thin-membraned balloon as a prototypical system that involves a doubly curved gross shape with large amplitude undulations. By probing its side profiles and horizontal cross-sections, we discover that the mean behavior of the film is the physical observable that is predicted by the geometric model, even when the buckled structures atop it are large. We then propose a minimal model for the horizontal cross-sections of the balloon, as independent elastic filaments subjected to an effective pinning potential around the mean shape. Despite the simplicity of our model, it reproduces a broad range of phenomena seen in the experiments, from how the morphology changes with pressure to the detailed shape of the wrinkles and folds. Our results establish a route to combine global and local features consistently over an enclosed surface, which could aid the design of inflatable structures, or provide insight into biological patterns.
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Affiliation(s)
- Mengfei He
- Department of Physics, Syracuse University, Syracuse, NY13244
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY13244
| | - Vincent Démery
- Gulliver, CNRS, École Supérieure de Physique et Chimie Industrielles de Paris, Paris Sciences et Lettres Research University, Paris75005, France
- Univ Lyon, École Normale Supérieure de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, LyonF-69342, France
| | - Joseph D. Paulsen
- Department of Physics, Syracuse University, Syracuse, NY13244
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY13244
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6
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Tanaka M, Montgomery SM, Yue L, Wei Y, Song Y, Nomura T, Qi HJ. Turing pattern-based design and fabrication of inflatable shape-morphing structures. SCIENCE ADVANCES 2023; 9:eade4381. [PMID: 36763653 PMCID: PMC9916983 DOI: 10.1126/sciadv.ade4381] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Accepted: 01/10/2023] [Indexed: 06/18/2023]
Abstract
Turing patterns are self-organizing stripes or spots widely found in biological systems and nature. Although inspiring, their applications are limited. Inflatable shape-morphing structures have attracted substantial research attention. Traditional inflatable structures use isotropic materials with geometrical features to achieve shape morphing. Recently, gradient-based optimization methods have been used to design these structures. These methods assume anisotropic materials whose orientation can vary freely. However, this assumption makes fabrication a considerable challenge by methods such as additive manufacturing, which print isotropic materials. Here, we present a methodology of using Turing patterns to bridge this gap. Specifically, we use Turing patterns to convert a design with distributed anisotropic materials to a distribution with two materials, which can be fabricated by grayscale digital light processing 3D printing. This work suggests that it is possible to apply patterns in biological systems and nature to engineering composites and offers new concepts for future material design.
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Affiliation(s)
- Masato Tanaka
- Toyota Research Institute of North America, Toyota Motor North America, Ann Arbor, MI 48105, USA
| | - S. Macrae Montgomery
- The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
| | - Liang Yue
- The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
| | - Yaochi Wei
- The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
| | - Yuyang Song
- Toyota Research Institute of North America, Toyota Motor North America, Ann Arbor, MI 48105, USA
| | - Tsuyoshi Nomura
- Toyota Central R&D Laboratories Inc. , Bunkyo-ku, Tokyo 112-0004, Japan
| | - H. Jerry Qi
- The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
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7
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Barber DM, Emrick T, Grason GM, Crosby AJ. Self-spinning filaments for autonomously linked microfibers. Nat Commun 2023; 14:625. [PMID: 36739283 PMCID: PMC9899204 DOI: 10.1038/s41467-023-36355-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2022] [Accepted: 01/30/2023] [Indexed: 02/06/2023] Open
Abstract
Filamentous bundles are ubiquitous in Nature, achieving highly adaptive functions and structural integrity from assembly of diverse mesoscale supramolecular elements. Engineering routes to synthetic, topologically integrated analogs demands precisely coordinated control of multiple filaments' shapes and positions, a major challenge when performed without complex machinery or labor-intensive processing. Here, we demonstrate a photocreasing design that encodes local curvature and twist into mesoscale polymer filaments, enabling their programmed transformation into target 3-dimensional geometries. Importantly, patterned photocreasing of filament arrays drives autonomous spinning to form linked filament bundles that are highly entangled and structurally robust. In individual filaments, photocreases unlock paths to arbitrary, 3-dimensional curves in space. Collectively, photocrease-mediated bundling establishes a transformative paradigm enabling smart, self-assembled mesostructures that mimic performance-differentiating structures in Nature (e.g., tendon and muscle fiber) and the macro-engineered world (e.g., rope).
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Affiliation(s)
- Dylan M Barber
- Polymer Science and Engineering Department, University of Massachusetts Amherst, Amherst, MA, 01003-9263, USA
| | - Todd Emrick
- Polymer Science and Engineering Department, University of Massachusetts Amherst, Amherst, MA, 01003-9263, USA.
| | - Gregory M Grason
- Polymer Science and Engineering Department, University of Massachusetts Amherst, Amherst, MA, 01003-9263, USA.
| | - Alfred J Crosby
- Polymer Science and Engineering Department, University of Massachusetts Amherst, Amherst, MA, 01003-9263, USA.
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Gao T, Siéfert E, DeSimone A, Roman B. Shape Programming by Modulating Actuation over Hierarchical Length Scales. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e2004515. [PMID: 33073431 DOI: 10.1002/adma.202004515] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Revised: 08/19/2020] [Indexed: 06/11/2023]
Abstract
Many active materials used in shape-morphing respond to an external stimulus by stretching or contracting along a director field. The programming of such actuators remains complex because of the single degree of freedom (the orientation) in local actuation. Here, texturing this field in zigzag patterns is shown to provide an extended family of biaxial active stretches out of an otherwise single uniaxial active deformation, opening a larger parameter space. By further modulating the zigzag patterns at the larger scale of the structure, its deployed shape can be controlled. This notion of texturing over hierarchical length scales follows geometrical principles, and is robust against changes in size and materials. The robustness of the approach is demonstrated by considering three different responsive materials: inextensible flat fabrics, channel-bearing elastomer (respectively, contracting and expanding perpendicularly to the director field when actuated pneumatically), and 3D-printed thermoplastic (composed of extruded filaments that contract when heated). It is shown that large-scale shape-morphing structures can be generated and that their geometry can be controlled with high accuracy.
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Affiliation(s)
- Tian Gao
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005, Paris, France
| | - Emmanuel Siéfert
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005, Paris, France
| | - Antonio DeSimone
- MathLab, SISSA-International School for Advanced Studies, 34136, Trieste, Italy
- The BioRobotics Institute and Department of Excellence in Robotics and AI, Scuola Superiore Sant'Anna, 56127, Pisa, Italy
| | - Benoît Roman
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005, Paris, France
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Siéfert E, Warner M. Inflationary routes to Gaussian curved topography. Proc Math Phys Eng Sci 2020; 476:20200047. [PMID: 32922150 DOI: 10.1098/rspa.2020.0047] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2020] [Accepted: 03/24/2020] [Indexed: 11/12/2022] Open
Abstract
Gaussian-curved shapes are obtained by inflating initially flat systems made of two superimposed strong and light thermoplastic impregnated fabric sheets heat-sealed together along a specific network of lines. The resulting inflated structures are light and very strong because they (largely) resist deformation by the intercession of stretch. Programmed patterns of channels vary either discretely through boundaries or continuously. The former give rise to faceted structures that are in effect non-isometric origami and that cannot unfold as in conventional folded structures since they present the localized angle deficit or surplus. Continuous variation of the channel direction in the form of spirals is examined, giving rise to curved shells. We solve the inverse problem consisting in finding a network of seam lines leading to a target axisymmetric shape on inflation. They too have strength from the metric changes that have been pneumatically driven, resistance to change being met with stretch and hence high forces like typical shells.
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Affiliation(s)
- Emmanuel Siéfert
- Laboratoire de Physique et Mécanique des Milieux Hétérogènes, CNRS UMR7636, Ecole Supérieure de Physique et Chimie Industrielles de Paris (ESPCI), Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Mark Warner
- Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge CB3 0HE, UK
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Siéfert E, Reyssat E, Bico J, Roman B. Programming stiff inflatable shells from planar patterned fabrics. SOFT MATTER 2020; 16:7898-7903. [PMID: 32729603 DOI: 10.1039/d0sm01041c] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Lack of stiffness often limits thin shape-shifting structures to small scales. The large in-plane transformations required to distort the metrics are indeed commonly achieved by using soft hydrogels or elastomers. We introduce here a versatile single-step method to shape-program stiff inflated structures, opening the door for numerous large scale applications, ranging from space deployable structures to emergency shelters. This technique relies on channel patterns obtained by heat-sealing superimposed flat quasi-inextensible fabric sheets. Inflating channels induces an anisotropic in-plane contraction and thus a possible change of Gaussian curvature. Seam lines, which act as a director field for the in-plane deformation, encode the shape of the deployed structure. We present three patterning methods to quantitatively and analytically program shells with non-Euclidean metrics. In addition to shapes, we describe with scaling laws the mechanical properties of the inflated structures. Large deployed structures can resist their weight, substantially broadening the palette of applications.
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Affiliation(s)
- Emmanuel Siéfert
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005, Paris, France.
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Jin L, Forte AE, Deng B, Rafsanjani A, Bertoldi K. Kirigami-Inspired Inflatables with Programmable Shapes. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e2001863. [PMID: 32627259 DOI: 10.1002/adma.202001863] [Citation(s) in RCA: 51] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Revised: 05/21/2020] [Accepted: 05/25/2020] [Indexed: 05/19/2023]
Abstract
Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet. Here, kirigami principles are exploited to design inflatables that can mimic target shapes upon pressurization. The system comprises a kirigami sheet embedded into an unstructured elastomeric membrane. First, it is shown that the inflated shape can be controlled by tuning the geometric parameters of the kirigami pattern. Then, by applying a simple optimization algorithm, the best parameters that enable the kirigami inflatables to transform into a family of target shapes at a given pressure are identified. Furthermore, thanks to the tessellated nature of the kirigami, it is shown that we can selectively manipulate the parameters of the single units to allow the reproduction of features at different scales and ultimately enable a more accurate mimicking of the target.
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Affiliation(s)
- Lishuai Jin
- Department of Mechanics, Tianjin University, Tianjin, 300350, China
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Antonio Elia Forte
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milan, 20133, Italy
| | - Bolei Deng
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | | | - Katia Bertoldi
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA, 02138, USA
- Kavli Institute, Harvard University, Cambridge, MA, 02138, USA
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