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Abstract and Figures
The shape transformation of some biological systems inspires scientists to create sophisticated structures at the nano- and macro- scales. However, to be useful in engineering, the mechanics of governing such a spontaneous, parallel and large deformation must be well understood. In this study, a kirigami approach is used to fold a bilayer planar sheet featuring a specific pattern into a buckliball under a certain thermal stimulus. Importantly, this prescribed spherical object can retract into a much smaller sphere due to constructive buckling caused by radially inward displacement. By minimizing the potential strain energy, we obtain a critical temperature, below which the patterned sheet exhibits identical principal curvatures everywhere in the self-folding procedure and above which buckling occurs. The applicability of the theoretical analysis to the self-folding of sheets with a diversity of patterns is verified by the finite element method.
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Supplementary resources (3)
... Similar to self-folding origami, kirigami can also self-deform under specific triggering methods. The basic means by which kirigami self-deforms is a nonuniform stress distribution that can be generated by different methods, such as bilayer materials with different properties, focused ion beams (FIBs), 10,161,172 temperature-responsive materials, 11,156,180,182 solvent-activated materials, 156 electroactive polymers, 179,188 magnetically activated materials, 178 shape-memory polymers, 177 photoactive materials, 163 and electrothermal materials. 173 The applications of self-deforming kirigami include shape morphing, 11,156,163,180,182 stents, 177 actuators for robotics, 161,163,178,179,188 MEMS, 173 tunable optical properties, 10,172 and tunable thermal expansion. ...
... The basic means by which kirigami self-deforms is a nonuniform stress distribution that can be generated by different methods, such as bilayer materials with different properties, focused ion beams (FIBs), 10,161,172 temperature-responsive materials, 11,156,180,182 solvent-activated materials, 156 electroactive polymers, 179,188 magnetically activated materials, 178 shape-memory polymers, 177 photoactive materials, 163 and electrothermal materials. 173 The applications of self-deforming kirigami include shape morphing, 11,156,163,180,182 stents, 177 actuators for robotics, 161,163,178,179,188 MEMS, 173 tunable optical properties, 10,172 and tunable thermal expansion. 11 Figure 6(g) shows propeller-shaped and pinwheel-shaped kirigamis made of gold film buckling under the triggering of an FIB. 10 Because of the tensile and compressive stresses introduced by the FIB, the kirigami pattern can be cut by a high-dose FIB and bent by a lowdose FIB. ...
Once merely ancient arts, origami (i.e., paper folding) and kirigami (i.e., paper cutting) have in recent years also become popular for building mechanical metamaterials and now provide valuable design guidelines. By means of folding and cutting, two-dimensional thin-film materials are transformed into complex three-dimensional structures and shapes with unique and programmable mechanical properties. In this review, mechanical metamaterials based on origami and/or kirigami are categorized into three groups: (i) origami-based ones (with folding only), (ii) kirigami-based ones (with cutting only), and (iii) hybrid origami-kirigami-based ones (with both folding and cutting). For each category, the deformation mechanisms, design principles, functions, and applications are reviewed from a mechanical perspective.
... By using projection microstereo lithography, hollow particles with a similar mechanism could be fabricated and applied to drug delivery under various stimuli, such as pH, temperature and humid. Recently, we created a bilayer planar sheet in a specific pattern (figure 8(c)) and validate it can self-fold into a buckliball under thermal stimulus [109]. Noted that it is a kind of kirigami approach and the pattern can be well designed to allow the film folding into wanted structures. ...
... (a) The progressively deformed shapes of a buckliball[107]; (b) numerical simulation of an improved buckliball with large volume retraction ratio[108]; (c) the folding of a planar sheet to create a buckliball[101,109]. ...
Being one of the commonest deformation modes for soft matters, shell buckling is the primary reason for the growth and nastic movement of many plants, as well as the formation of complex natural morphology. On-demand regulation of buckling-induced deformation associated with wrinkling, ruffling, folding, creasing and delaminating has profound implications for diverse scopes, which can be seen in its broad applications in microfabrication, 4D printing, actuator and drug delivery. This paper reviews the recent remarkable developments in the shell buckling of soft matters to explain the most representative natural morphogenesis from the perspectives of theoretical analysis in continuum mechanics, finite element analysis, and experimental validations. Imitation of buckling-induced shape transformation and its applications are also discussed for the innovations of sophisticated materials and devices in future.
... Among all kinds of foldable polyhedrons whose edges are all equal in length, it can be seen from Figure 5E that the deformation of a regular octahedron is the simplest, and its square hole after expanding is the largest which is helpful for the target to swim in. In addition, although the deformation mode of the basic deformable polyhedrons shown in Figure 5E is identical to the previous research about "the Buckliball," [24][25][26][27] the ways to achieve its deformability are different. More specifically, the origami method introduced in this article (convex every regular face into several rigid kite-shaped faces) ensures more definite trajectories, better bistability, and better controllability. ...
In the marine biological sampling, the noncontact polyhedral gripper was initially developed for the purpose of capturing brittle animals and delicate soft‐bodied organisms. However, the auxiliary driving rods of earlier polyhedral grippers make their structure complex; and the unidirectional surrounding capture process makes it simple to generate water flow with less capture effect. In this paper, an origami polyhedral gripper for midwater sampling is introduced, along with its fabrication, analysis, material selection, and size parameter calculation process. The capture process is designed to be omnidirectional surrounding; therefore the generated water flow can be reduced. And the whole mechanism is bi‐stable and only needs one actuator to operate. Capture experiments on pet fish with fragile tails were conducted on an ROV (Remotely Operated Vehicle) and on simply constructing artificial arms to prove its feasibility and high adaptability. Overall, the unit mechanism of this gripper is analyzed using the Screw theory to show how it has a bistate feature. And using the same origami‐structural unit, additional foldable polyhedral structures with the same folding modes are also introduced. This article is protected by copyright. All rights reserved.
... The beauty of nature is manifested through the fascinating structures of botanical/animal organs, such as furcate [1], lacunar [2] and reticular [3] structures, the formation of which has aroused considerable curiosity among scientists for decades [4]. Through the long-term process of evolution, the distributions of leaf veins have naturally developed into well-organized structures [5]. ...
The stiffness and heat dissipation of thin planar structures in industrial engineering are taken as the background for this research. Plant leaves with various vein patterns, such as tobacco (Nicotiana tabacum L.) and chili (Capsicum annuum L.) leaves, are treated as the research objects. Through a combination of morphological and mechanical analysis, the distribution patterns and properties of leaf veins are mathematically characterized. A topological optimization algorithm is employed to simulate the vein growth process, thus revealing the effects of the mechanical and biological properties of different leaves on their vein morphologies. Additionally, the angles between the main and secondary veins are controlled to satisfy biological constraints. This comprehensive exploration of vein morphological formation can serve as a reference for the design of bionic thin planar structures in engineering.
... Fused deposition modeling (FDM), a fast and direct additive manufacturing technology, prints structures by accumulating ejected warmed thermoplastic fibers layerby-layer [1] and has been widely adopted in prototype fabrication [2], biomedical engineering [3,4], bionic structures [5], electronic devices [6], and drug delivery [7]. This rapid manufacturing technique is becoming a popular area of research that has been advanced by innovative technologies, methods, and materials. ...
Additive manufacturing has the potential to provide novel solutions for fabricating complex structures. However, one of the main obstacles for such methods is the anisotropic mechanical properties of the manufactured product, which hinder the popularization of additive manufacturing in modern industries. Here, a simple yet versatile algorithm is introduced to produce isotropic products via optimizing the printing path. In this method, the workpiece is first separated into distinct areas in terms of the printing sequence, which increases the efficiency of the fabrication process. Subsequently, the printing path is schemed in each sub-region to allow a short extrusion length and low number of start-stop processes. Finally, this maze-like printing path is revised through a series of tensile tests and fracture surface analyses to validate the isotropy. Bending and indentation tests demonstrate that the samples present distinguished properties in terms of strength and isotropy in mechanical properties. Moreover, numerical and physical tests are implemented for validating the advantage of this maze-like pattern in preventing warping caused by residual stress. This work may play a significant role in printing molds that require isotropic properties.
... The fundamental principle of origami is to transform a flat sheet square (2-D) of paper into a finished sculpture (3-D) through folding and sculpting techniques along pre-defined creases. Because of its unique properties, origami has been imitated and developed to design foldable mechanisms (Hanna et al., 2014), self-deployable structures (Delimont et al., 2015), robots (Jayaram and Full, 2016), self-folding structures (Na et al., 2015), metamaterials (Overbelde et al., 2017), energy absorbing structures (Yang et al., 2016 and to solve plant structure folding (Couturier et al., 2013), soft matter folding (Lin et al., 2016) and even protein folding problems (Gethin and Sambrook, 1992). From an engineering viewpoint, mechanical properties of the crease for design-ing origami structures are of significant importance, which should be fully understood and characterised. ...
In this study the mechanical behaviour of a creased thin strip under opposite-sense bending was investigated.
It was found that a simple crease, which led to the increase of the second moment of area, could
significantly alter the overall mechanical behaviour of a thin strip, for example the peak moment could be increased
by 100 times. The crease was treated as a cylindrical segment of a small radius. Parametric studies
demonstrated that the geometry of the strip could strongly influence its flexural behaviour. We showed that the
uniform thickness and the radius of the creased segment had the greatest and the least influence on the mechanical
behaviour, respectively. We further revealed that material properties could dramatically affect the overall
mechanical behaviour of the creased strip by gradually changing the material from being linear elastic to elasticperfect
plastic. After the formation of the fold, the moment of the two ends of the strip differed considerably
when the elasto-plastic materials were used, especially for materials with smaller tangent modulus in the plastic
range. The deformation patterns of the thin strips from the finite element simulations were verified by physical
models made of thin metal strips. The findings from this study provide useful information for designing origami
structures for engineering applications using creased thin strips.
This paper presents an optimization method to systematically design human-made corals using the technique of solid isotropic material with the penaliza-tion. In optimization, we minimized the squared norm of the carbon gradient and considered the volume constraint and the length constraint. We homogeneously dented optimization results using a surface mapping method to provide shelters for polyps, which widely exist in natural corals like the antho-cyanins. A computational fluid dynamics investigation based on the lattice Boltzmann method illustrated that the branches of the optimized configuration could shield polyps from ocean currents and afford sufficient nutrition. Eventually, we prototyped samples by digital light processing printer with an optimum mixture ratio of biologically compatible calcium carbonate and photosensitive material. Examples show the tropism of marine organisms in human-made corals is akin to the natural ones. The proposed method allows designing human-made corals and is crucial for environmental remediation.
Origami that can form various shapes by setting simple
creases on the paper and folding along these creases has a lot of
applications from the fields of art to engineering. The inverse problem of
origami that determines the distribution of creases based on the desired
shape is very complicated. In this paper, we use theoretical kinematics to
systematically analyse an inverse folding problem of a toy about how to fold
a piece of paper into a disc through a smaller hole without breaking it. The
results show that some four-crease and six-crease patterns can achieve the
expected function, and they can be easily folded with 1 degree of freedom
(DOF). It not only opens up a new way to solve the inverse folding problem
but also helps students to understand mechanisms and machine theory.
The paper A generic geometric transformation that unifies a wide range of natural and abstract shapes [1] introduced the Superformula, a generalization of circles and the Pythagorean Theorem, based on work of the French mathematician Gabriel Lamé (1795-1860). In the literature one finds names like Superformula, Gielis Superformula or Gielis curves, surfaces and (sub-) manifolds and Gielis transformations. The former was used in the article, as generalization of Lamé curves, also known as supercircles and superellipses.
Its origin is in the description of botanical shapes, but it is a fundamental equation that finds applications in many directions. In the past two decades a variety of papers, books and book chapters, theses and patents were published using this transformation, in the fields of mathematics, physics, biology, technology and education. It is the purpose of this article to give an updated overview and list of such applications and publications.
Using bibliometric data and citation indices, the use of the formula is divided into three categories, namely Mathematics, Science and Technology. The Science category is subdivided in biology, psychology and physics, and for Technology six categories are defined, namely 1) antennas, electronics and metamaterials, 2) nanotechnology, 3) applied physics, 4) mechanics and mechanotronics, 5) computer graphics and modeling, and 6) computer vision and datamining. This is also testimony to the unifying power.
In total close close to 500 references are returned by Googlescholar, and in total over 500 have been used to build the database. This overview also includes a full list of these publications, in Endnote and in Excel format . Given this wide diversity and citations, the database aims researchers are in finding work in similar or distant areas.
The number of references marks the paper as extremely highly cited. It is special for two reasons. First, 70-80 % of all papers receive less than 10 citations (almost half of the papers are never cited). With this number of references this puts the paper in the top 1,5 % of all papers published. Second, the references come from many directions, from quantum to astronomy, from mechanical design to nano-optics, and from pure math to algorithms for the best buy.
Electrically conductive cementitious composite (ECCC) can be utilized in traffic detection, structural health monitoring (SHM), and pavement deicing. Graphite is a popular conductive filler given its outstanding electrical resistance behavior, but its flat micro‐surface decreases the friction resistance, reducing mechanical strength. However, slag solids can substitute part of the graphite with their considerable conductivity and superior mechanical characteristics. In this research, 27 ECCC composites are developed incorporated by combined graphite powder (GP), blast furnace slag (GGBS), and steel slag (SS). Flexural, unconfined compressive strength (UCS) experiments, and resistance experiments with failure mode evaluations are carried out to explore the influence of proposed conductive fillers with different fractions. Results show the graphite strongly improves conductivity but dramatically reduces mechanical performance. Both steel slag and GGBS reduced the compressive and flexural strength after their replacement ratio exceeded 20%. Additionally, compared with GGBS, SS demonstrated a better influence on mechanical and conductive performance. A 15 wt% ratio of GGBS, 20 wt% of SS, and 4 wt% of GP are explored as the optimum design with 3.4 MPa of flexural strength, 36 MPa of compressive strength, and 7,779 Ω cm of resistance. Lastly, a microstructural investigation is conducted to explore the mechanical and conductive mechanism of ECCC.
Reconfigurable devices, whose shape can be drastically altered, are central to expandable shelters, deployable space structures, reversible encapsulation systems and medical tools and robots. All these applications require structures whose shape can be actively controlled, both for deployment and to conform to the surrounding environment. While most current reconfigurable designs are application specific, here we present a mechanical metamaterial with tunable shape, volume and stiffness. Our approach exploits a simple modular origami-like design consisting of rigid faces and hinges, which are connected to form a periodic structure consisting of extruded cubes. We show both analytically and experimentally that the transformable metamaterial has three degrees of freedom, which can be actively deformed into numerous specific shapes through embedded actuation. The proposed metamaterial can be used to realize transformable structures with arbitrary architectures, highlighting a robust strategy for the design of reconfigurable devices over a wide range of length scales.
Origami, the ancient art of paper folding, has inspired the design of engineering devices and structures for decades. The underlying principles of origami are very general, which has led to applications ranging from cardboard containers to deployable space structures. More recently, researchers have become interested in the use of active materials (i.e., those that convert various forms of energy into mechanical work) to effect the desired folding behavior. When used in a suitable geometry, active materials allow engineers to create self-folding structures. Such structures are capable of performing folding and/or unfolding operations without being kinematically manipulated by external forces or moments. This is advantageous for many applications including space systems, underwater robotics, small scale devices, and self-assembling systems. This article is a survey and analysis of prior work on active self-folding structures as well as methods and tools available for the design of folding structures in general and self-folding structures in particular. The goal is to provide researchers and practitioners with a systematic view of the state-of-the-art in this important and evolving area. Unifying structural principles for active self-folding structures are identified and used as a basis for a quantitative and qualitative comparison of numerous classes of active materials. Design considerations specific to folded structures are examined, including the issues of crease pattern identification and fold kinematics. Although few tools have been created with active materials in mind, many of them are useful in the overall design process for active self-folding structures. Finally, the article concludes with a discussion of open questions for the field of origami-inspired engineering.
Combination of soft active hydrogels with hard passive polymers gives
rise to all-polymer composites. The hydrogel is sensitive to external
stimuli while the passive polymer is inert. Utilizing the different
behaviors of two materials subject to environmental variation, for
example temperature, results in self-folding soft machines. We report
our efforts to model the programmable deformation of self-folding
structures with temperature-sensitive hydrogels. The self-folding
structures are realized either by constructing a bilayer structure or by
incorporating hydrogels as hinges. The methodology and the results may
aid the design, control and fabrication of 3D complex structures from 2D
simple configurations through self-assembly.
Combining the physical principle of actuators with the basic concept of photonic crystals, colour-tunable three-dimensional (3D) photonic actuators were successfully fabricated. By controlling the d-spacings and the refractive index contrasts of the self-assembled 3D colloidal photonic crystals, colours of the photonic actuators were tuned. Various shapes of these 3D actuating objects were constructed by transforming the programmed 2D structures via bending, twisting and folding mechanisms. These 2D structures were first programmed by breaking the symmetry. The selective swellings were then applied as driving forces to control the shapes and colours of the photonic actuators. Scroll photonic actuators had been first demonstrated by bending the traditional 2D cantilever structure (K.-U. Jeong, et al., J.Mater.Chem., 2009, 19, 1956). By breaking the symmetry of a cantilever structure perpendicular to its long axis, polypeptide-/DNA-like 3D helical photonic actuators were obtained from the programmed 2D structure via twisting processes. Both left- and right-handed scrolls and helices with various colours can be achieved by changing the polarity of solvents. Different types of 3D actuators, such as cube, pyramid and phlat ball, were also demonstrated via the folding mechanism. The reversible 3D photonic actuators transformed from the programmed 2D structures via the bending, twisting and folding mechanisms may be applied in the field of mechanical actuators, and optoelectronic and bio-mimetic devices.
Shape change is a prevalent function apparent in a diverse set of natural structures, including seed dispersal units, climbing plants and carnivorous plants. Many of these natural materials change shape by using cellulose microfibrils at specific orientations to anisotropically restrict the swelling/shrinkage of their organic matrices upon external stimuli. This is in contrast to the material-specific mechanisms found in synthetic shape-memory systems. Here we propose a robust and universal method to replicate this unusual shape-changing mechanism of natural systems in artificial bioinspired composites. The technique is based upon the remote control of the orientation of reinforcing inorganic particles within the composite using a weak external magnetic field. Combining this reinforcement orientational control with swellable/shrinkable polymer matrices enables the creation of composites whose shape change can be programmed into the material's microstructure rather than externally imposed. Such bioinspired approach can generate composites with unusual reversibility, twisting effects and site-specific programmable shape changes.
This paper presents a system for computer based interactive simulation of origami, based on rigid origami model. Our system shows the continuous process of fold-ing a piece of paper into a folded shape by calculating the configuration from the crease pattern. The configuration of the model is represented by crease angles, and the trajectory is calculated by projecting angles motion to the constrained space. Additionally, polygons are triangulated and crease lines are adjusted in order to make the model more flexible. Flexible motion and comprehensible representation of origami help users to understand the structure of the model and to fold the model from a crease pattern.
We introduce a class of continuum shell structures, the Buckliball, which undergoes a structural transformation induced by buckling under pressure loading. The geometry of the Buckliball comprises a spherical shell patterned with a regular array of circular voids. In order for the pattern transformation to be induced by buckling, the possible number and arrangement of these voids are found to be restricted to five specific configurations. Below a critical internal pressure, the narrow ligaments between the voids buckle, leading to a cooperative buckling cascade of the skeleton of the ball. This ligament buckling leads to closure of the voids and a reduction of the total volume of the shell by up to 54%, while remaining spherical, thereby opening the possibility of encapsulation. We use a combination of precision desktop-scale experiments, finite element simulations, and scaling analyses to explore the underlying mechanics of these foldable structures, finding excellent qualitative and quantitative agreement. Given that this folding mechanism is induced by a mechanical instability, our Buckliball opens the possibility for reversible encapsulation, over a wide range of length scales.
This paper considers planning and control algorithms that enable a programmable sheet to realize different shapes by autonomous folding. Prior work on self-reconfiguring machines has considered modular systems in which independent units coordinate with their neighbors to realize a desired shape. A key limitation in these prior systems is the typically many operations to make and break connections with neighbors, which lead to brittle performance. We seek to mitigate these difficulties through the unique concept of self-folding origami with a universal fixed set of hinges. This approach exploits a single sheet composed of interconnected triangular sections. The sheet is able to fold into a set of predetermined shapes using embedded actuation.
We describe the planning algorithms underlying these self-folding sheets, forming a new family of reconfigurable robots that fold themselves into origami by actuating edges to fold by desired angles at desired times. Given a flat sheet, the set of hinges, and a desired folded state for the sheet, the algorithms (1) plan a continuous folding motion into the desired state, (2) discretize this motion into a practicable sequence of phases, (3) overlay these patterns and factor the steps into a minimum set of groups, and (4) automatically plan the location of actuators and threads on the sheet for implementing the shape-formation control.
Self-assembly has emerged as a paradigm for highly parallel fabrication of complex three-dimensional structures. However, there are few principles that guide a priori design, yield, and defect tolerance of self-assembling structures. We examine with experiment and theory the geometric principles that underlie self-folding of submillimeter-scale higher polyhedra from two-dimensional nets. In particular, we computationally search for nets within a large set of possibilities and then test these nets experimentally. Our main findings are that (i) compactness is a simple and effective design principle for maximizing the yield of self-folding polyhedra; and (ii) shortest paths from 2D nets to 3D polyhedra in the configuration space are important for rationalizing experimentally observed folding pathways. Our work provides a model problem amenable to experimental and theoretical analysis of design principles and pathways in self-assembly.
To study forms in plants and other living organisms, several mathematical tools are available, most of which are general tools that do not take into account valuable biological information. In this report I present a new geometrical approach for modeling and understanding various abstract, natural, and man-made shapes. Starting from the concept of the circle, I show that a large variety of shapes can be described by a single and simple geometrical equation, the Superformula. Modification of the parameters permits the generation of various natural polygons. For example, applying the equation to logarithmic or trigonometric functions modifies the metrics of these functions and all associated graphs. As a unifying framework, all these shapes are proven to be circles in their internal metrics, and the Superformula provides the precise mathematical relation between Euclidean measurements and the internal non-Euclidean metrics of shapes. Looking beyond Euclidean circles and Pythagorean measures reveals a novel and powerful way to study natural forms and phenomena.
Programmable matter is a material whose properties can be programmed to achieve specific shapes or stiffnesses upon command. This concept requires constituent elements to interact and rearrange intelligently in order to meet the goal. This paper considers achieving programmable sheets that can form themselves in different shapes autonomously by folding. Past approaches to creating transforming machines have been limited by the small feature sizes, the large number of components, and the associated complexity of communication among the units. We seek to mitigate these difficulties through the unique concept of self-folding origami with universal crease patterns. This approach exploits a single sheet composed of interconnected triangular sections. The sheet is able to fold into a set of predetermined shapes using embedded actuation. To implement this self-folding origami concept, we have developed a scalable end-to-end planning and fabrication process. Given a set of desired objects, the system computes an optimized design for a single sheet and multiple controllers to achieve each of the desired objects. The material, called programmable matter by folding, is an example of a system capable of achieving multiple shapes for multiple functions.
(Figure Presented) Printed origami structures are fabricated by combining direct-write assembly of planar lattices with a wet-folding origami technique. This novel approach provides a low-cost, versatile route to create threedimensional structures from diverse materials, whose shapes range from simple polyhedra to intricate origami forms.
Long leaves in terrestrial plants and their submarine counterparts, algal blades, have a typical, saddle-like midsurface and rippled edges. To understand the origin of these morphologies, we dissect leaves and differentially stretch foam ribbons to show that these shapes arise from a simple cause, the elastic relaxation via bending that follows either differential growth (in leaves) or differential stretching past the yield point (in ribbons). We quantify these different modalities in terms of a mathematical model for the shape of an initially flat elastic sheet with lateral gradients in longitudinal growth. By using a combination of scaling concepts, stability analysis, and numerical simulations, we map out the shape space for these growing ribbons and find that as the relative growth strain is increased, a long flat lamina deforms to a saddle shape and/or develops undulations that may lead to strongly localized ripples as the growth strain is localized to the edge of the leaf. Our theory delineates the geometric and growth control parameters that determine the shape space of finite laminae and thus allows for a comparative study of elongated leaf morphology.
A central challenge in nanotechnology is the parallel fabrication of complex geometries for nanodevices. Here we report a general method for arranging single-walled carbon nanotubes in two dimensions using DNA origami-a technique in which a long single strand of DNA is folded into a predetermined shape. We synthesize rectangular origami templates ( approximately 75 nm x 95 nm) that display two lines of single-stranded DNA 'hooks' in a cross pattern with approximately 6 nm resolution. The perpendicular lines of hooks serve as sequence-specific binding sites for two types of nanotubes, each functionalized non-covalently with a distinct DNA linker molecule. The hook-binding domain of each linker is protected to ensure efficient hybridization. When origami templates and DNA-functionalized nanotubes are mixed, strand displacement-mediated deprotection and binding aligns the nanotubes into cross-junctions. Of several cross-junctions synthesized by this method, one demonstrated stable field-effect transistor-like behaviour. In such organizations of electronic components, DNA origami serves as a programmable nanobreadboard; thus, DNA origami may allow the rapid prototyping of complex nanotube-based structures.
Modern computer simulations make stress analysis easy. As they continue to replace classical mathematical methods of analysis, these software programs require users to have a solid understanding of the fundamental principles on which they are based. Develop Intuitive Ability to Identify and Avoid Physically Meaningless Predictions Applied Mechanics of Solids is a powerful tool for understanding how to take advantage of these revolutionary computer advances in the field of solid mechanics. Beginning with a description of the physical and mathematical laws that govern deformation in solids, the text presents modern constitutive equations, as well as analytical and computational methods of stress analysis and fracture mechanics. It also addresses the nonlinear theory of deformable rods, membranes, plates, and shells, and solutions to important boundary and initial value problems in solid mechanics. The author uses the step-by-step manner of a blackboard lecture to explain problem solving methods, often providing the solution to a problem before its derivation is presented. This format will be useful for practicing engineers and scientists who need a quick review of some aspect of solid mechanics, as well as for instructors and students. Select and Combine Topics Using Self-Contained Modules and Subsections Borrowing from the classical literature on linear elasticity, plasticity, and structural mechanics, this book: • Introduces concepts, analytical techniques, and numerical methods used to analyze deformation, stress, and failure in materials or components • Discusses the use of finite element software for stress analysis • Assesses simple analytical solutions to explain how to set up properly posed boundary and initial-value problems • Provides an understanding of algorithms implemented in software code Complemented by the author's website, which features problem sets and sample code for self study, this book offers a crucial overview of problem solving for solid mechanics. It will help readers make optimal use of commercial finite element programs to achieve the most accurate prediction results possible.
Significance
Existing options in three-dimensional (3D) assembly of micro/nanomaterials are constrained by a narrow accessible range of materials and/or 3D geometries. Here we introduce concepts for a form of Kirigami for the precise, mechanically driven assembly of 3D mesostructures from 2D micro/nanomembranes with strategically designed geometries and patterns of cuts. Theoretical and experimental studies in a broad set of examples demonstrate the applicability across length scales from macro to micro and nano, in materials ranging from monocrystalline silicon to metal and plastic, with levels of topographical complexity that significantly exceed those possible with other schemes. The resulting engineering options in functional 3D mesostructures have important implications for construction of advanced micro/nanosystems technologies.
Buckling of soft matter is ubiquitous in nature and has attracted increasing interest recently. This paper studies the retractile behaviors of a spherical shell perforated by sophisticated apertures, attributed to the buckling-induced large deformation. The buckling patterns observed in experiments were reproduced in computational modeling by imposing velocity-controlled loads and eigenmode-affine geometric imperfection. It was found that the buckling behaviors were topologically sensitive with respect to the shape of dimple (aperture). The shell with rounded-square apertures had the maximal volume retraction ratio as well as the lowest energy consumption. An effective experimental procedure was established and the simulation results were validated in this study. Reconfigurable and reversible devices can rapidly respond to mechanical, thermal, chemical, electromagnetic and optical stimuli by changing their shapes and functionalities. Such active structures capable of smartly adapting to ambient environment widely exist in nature. For instance, some viruses can expand and retract their shell-like bodies by opening and closing the external apertures when the environmental pH changes 1,2
Biomimetics faces a continual challenge of how to bridge the gap between what Nature has so effectively evolved and
the current tools and materials that engineers and scientists can exploit. Kirigami, from the Japanese ‘cut’ and ‘paper’, is
a method of design where laminar materials are cut and then forced out-of-plane to yield 3D structures. Kirimimetic
design provides a convenient and relatively closed design space within which to replicate some of the most interesting
niche biological mechanisms. These include complex flexing organelles such as cilia in algae, energy storage and
buckled structures in plants, and organic appendages that actuate out-of-plane such as the myoneme of the Vorticella
protozoa. Where traditional kirigami employs passive materials which must be forced to transition to higher dimensions,
we can exploit planar smart actuators and artificial muscles to create self-actuating kirigami structures. Here we review
biomimetics with respect to the kirigami design and fabrication methods and examine how smart materials, including
electroactive polymers and shape memory polymers, can be used to realise effective biomimetic components for robotic,
deployable structures and engineering systems. One-way actuation, for example using shape memory polymers, can
yield complete self-deploying structures. Bi-directional actuation, in contrast, can be exploited to mimic fundamental
biological mechanisms such as thrust generation and fluid control. We present recent examples of kirigami robotic
mechanisms and actuators and discuss planar fabrication methods, including rapid prototyping and 3D printing, and how
current technologies, and their limitations, affect Kirigami robotics.
Significance
Most materials can be stretched to a small degree, depending on their elastic limits and failure properties. For most materials the maximum elastic dilatation is very small, implying that the macroscopic shapes to which an elastic body can be deformed is severely limited. The present work addresses the simple modification of any material via hierarchical cut patterns to allow for extremely large strains and shape changes and a large range of macroscopic shapes. This is an important step in the development of shape-programmable materials. We provide the mathematical foundation, simulation results, and experimental demonstrations of the concept of fractal cut. This approach effectively broadens the design space for engineered materials for applications ranging from flexible/stretchable devices and photonic materials to bioscaffolds.
Self-folding microscale origami patterns are demonstrated in polymer films with control over mountain/valley assignments and fold angles using trilayers of photo-crosslinkable copolymers with a temperature-sensitive hydrogel as the middle layer. The characteristic size scale of the folds W = 30 μm and figure of merit A/ W (2) ≈ 5000, demonstrated here represent substantial advances in the fabrication of self-folding origami.
Self-folding is an approach used frequently in nature for the efficient fabrication of structures, but is seldom used in engineered systems. Here, self-folding origami are presented, which consist of shape memory composites that are activated with uniform heating in an oven. These composites are rapidly fabricated using inexpensive materials and tools. The folding mechanism based on the in-plane contraction of a sheet of shape memory polymer is modeled, and parameters for the design of composites that self-fold into target shapes are characterized. Four self-folding shapes are demonstrated: a cube, an icosahedron, a flower, and a Miura pattern; each of which is activated in an oven in less than 4 min. Self-sealing is also investigated using hot melt adhesive, and the resulting structures are found to bear up to twice the load of unsealed structures.
Here we present the design of a 1.27g quadrupedal microrobot manufactured using “Pop-up book MEMS” the first such device capable of locomotion. Implementing popup assembly techniques enables manufacturing of the robot's exoskeleton and drivetrain transmissions from a single 23-layer laminate. Its demonstrated capabilities include payload capacity greater than 1.35g (106% of body mass), maneuverability on flat terrain, and high-speed locomotion up to 37cm/s. Additionally, locomotion performance is compared to a hand-assembled quadruped with similar design parameters. The results demonstrate that the pop-up manufacturing methodology enables more complex mechanisms while simultaneously increasing performance over hand-assembled alternatives.
We report on a therapeutic approach using thermo-responsive multi-fingered drug eluting devices. These therapeutic grippers referred to as theragrippers are shaped using photolithographic patterning and are composed of rigid poly(propylene fumarate) segments and stimuli-responsive poly(N-isopropylacrylamide-co-acrylic acid) hinges. They close above 32 °C allowing them to spontaneously grip onto tissue when introduced from a cold state into the body. Due to porosity in the grippers, theragrippers could also be loaded with fluorescent dyes and commercial drugs such as mesalamine and doxorubicin, which eluted from the grippers for up to seven days with first order release kinetics. In an in vitro model, theragrippers enhanced delivery of doxorubicin as compared to a control patch. We also released theragrippers into a live pig and visualized release of dye in the stomach. The design of such tissue gripping drug delivery devices offers an effective strategy for sustained release of drugs with immediate applicability in the gastrointestinal tract.
Fabrication of 3D objects using folding of thin films is a novel and very attractive research field. The manuscript overviews recent advances in development and application of polymer films, which are able to fold and form 3D structures.
A previously developed geometrically nonlinear stress-curvature relation is expanded in this paper to allow for a less restrictive approximation of the midplane strains in a thin film/substrate system. The previous analysis is based on a minimization of the total strain energy and predicts a bifurcation in shape as the magnitude of intrinsic film stress increases. It is reviewed here and three new cases are presented. Expanding the approximating polynomials for the normal midplane strains and , has a small effect on the solution. However, allowing the midplane shear strain, , to be nonzero has a pronounced effect on the solution, particularly in the stress region near the bifurcation point.
Thermally activated, untethered microgrippers can reach narrow conduits in the body and be used to excise tissue for diagnostic analyses. As depicted in the figure, the feasibility of an in vivo biopsy of the porcine bile duct using untethered microgrippers is demonstrated.
Ion processing of the reactive surface of a free-standing polycrystalline metal film induces a flow of atoms into grain boundaries, resulting in plastic deformation. A thorough experimental and theoretical analysis of this process is presented, along with the demonstration of novel engineering concepts for precisely-controlled 3D-assembly at micro- and nanoscopic scales.
Table of Contents Introduction Building Blocks Elephant Design Traditional Bases Folding Instructions Stealth Fighter. Snail. Valentine. Ruby-Throated Hummingbird. Baby. Splitting Points Folding Instructions Pteranodon. Goatfish. Grafting Folding Instructions Songbird 1. KNL Dragon. Lizard. Tree Frog. Dancing Crane. Pattern Grafting Folding Instructions Turtle. Western Pond Turtle. Koi. Tiling Folding Instructions Pegasus Circle Packing Folding Instructions Emu. Songbird 2. Molecules Folding Instructions Orchid Blossom. Silverfish. Tree Theory Folding Instructions Alamo Stallion. Roosevelt Elk. Box Pleating Folding Instructions Organist. Black Forest Cuckoo Clock. Uniaxial Box Pleating Folding Instructions Bull Moose Polygon Packing Crease Patterns Flying Walking Stick. Salt Creek Tiger Beetle. Longhorn Beetle. Camel Spider. Water Strider. Scarab Beetle. Cicada Nymph. Scarab HP. Cyclomatus metallifer. Scorpion HP. Euthysanius Beetle. Spur-Legged Dung Beetle. Hybrid Bases Folding Instructions African Elephant References Glossary of Terms Index
Self-folding broadly refers to self-assembly processes wherein thin films or interconnected planar templates curve, roll-up or fold into three dimensional (3D) structures such as cylindrical tubes, spirals, corrugated sheets or polyhedra. The process has been demonstrated with metallic, semiconducting and polymeric films and has been used to curve tubes with diameters as small as 2nm and fold polyhedra as small as 100nm, with a surface patterning resolution of 15nm. Self-folding methods are important for drug delivery applications since they provide a means to realize 3D, biocompatible, all-polymeric containers with well-tailored composition, size, shape, wall thickness, porosity, surface patterns and chemistry. Self-folding is also a highly parallel process, and it is possible to encapsulate or self-load therapeutic cargo during assembly. A variety of therapeutic cargos such as small molecules, peptides, proteins, bacteria, fungi and mammalian cells have been encapsulated in self-folded polymeric containers. In this review, we focus on self-folding of all-polymeric containers. We discuss the mechanistic aspects of self-folding of polymeric containers driven by differential stresses or surface tension forces, the applications of self-folding polymers in drug delivery and we outline future challenges.
Nanoscale self-folding of electron-beam lithography patterned templates is used to create 3D devices for optics and biosensing.
Fabrication of 3D electronic structures in the micrometer-to-millimeter range is extremely challenging due to the inherently 2D nature of most conventional wafer-based fabrication methods. Self-assembly, and the related method of self-folding of planar patterned membranes, provide a promising means to solve this problem. Here, we investigate self-assembly processes driven by wetting interactions to shape the contour of a functional, nonplanar photovoltaic (PV) device. A mechanics model based on the theory of thin plates is developed to identify the critical conditions for self-folding of different 2D geometrical shapes. This strategy is demonstrated for specifically designed millimeter-scale silicon objects, which are self-assembled into spherical, and other 3D shapes and integrated into fully functional light-trapping PV devices. The resulting 3D devices offer a promising way to efficiently harvest solar energy in thin cells using concentrator microarrays that function without active light tracking systems.
Smart materials: Preparation of PNIPAM core-shell microgels, with a single metal or silica nanoparticle in the core and low polydispersity, are achieved (see picture; cores are silica particles). A versatile method is used, which could be applied to other types of nanoparticles. (Figure Presented).
And The Modeling Of Leaves: An Interactive Computer Application PhD Degree Thesis thesis
- S Jazebi
- Kirigami Origami
Jazebi, S. Origami, Kirigami, And The Modeling Of Leaves: An Interactive Computer Application PhD Degree Thesis thesis. The
University of Calgary (2012).
Self-assembly of carbon nanotubes into two-dimensional geometries using DNA origami templates
- H T Maune
- HT Maune