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Designing novel structures with hierarchically synchronized deformations
Abstract
In this paper, we propose a general mechanism to realize a uniform global motion of an n-level hierarchical structure constructed by base components of various shapes, which has only n degrees of freedom. The uniform global motion of the components at the same level of hierarchy is synchronized and independent of movements at other levels. The significantly reduced number of degrees of freedom is achieved by introducing a parallelogram linkage loop to the structure while the hierarchy is obtained from the similarity between the structure and its representative components at different levels. Theoretical analysis reveals the kinematic equations that govern the expansion and retraction of the deployable devices. Numerical simulation and physical prototyping verify the theoretical prediction. This study paves a way towards designing deployable and easily controllable devices and structures for many applications in aeronautics, electronics, optics, and MEMS.
Supplementary resources (4)
... To solve the problem that monostable materials cannot maintain the post-deformation shape after load removal, Rafsanjani et al [41], inspired by the ancient geometric patterns of square and triangular lattice arrangements, proposed plastic, and structural bistable rotationally auxetic structures as shown in figure 5(d), and conducted in-depth investigations on both square and triangular bistable auxetic structures. In addition, this type of rotational stiffness principle has been applied to hierarchical structures with many degrees of freedom [42]. ...
... CC BY 4.0. (e) Hierarchy structure[42], Reprinted from[42], Copyright (2017), with permission from Elsevier. (f) 3D rotating rigid mechanism[43]. ...
... CC BY 4.0. (e) Hierarchy structure[42], Reprinted from[42], Copyright (2017), with permission from Elsevier. (f) 3D rotating rigid mechanism[43]. ...
Auxetic or negative Poisson's ratio (NPR) materials and structures are exemplary mechanical meta-materials, possessing greater energy absorption capacity, stronger indentation resistance, and other advantages. Due to their unique indentation resistance, auxetic meta-materials have tremendous potential for use in impact engineering applications. To unveil the categories, characteristics, and applications of auxetic meta-materials, this study expounded upon the basic principles of auxeticity at the structural level and its associated mechanical properties. Additionally, it outlined the typical applications within the fields of medicine, automotive manufacturing, protective gear, and garments. The auxetic honeycomb structures of interest were first classified into three types: re-entrant, chiral, and rotational rigid structures. The auxetic mechanism and mechanical properties of these structures were then discussed and compared. Furthermore, by examining their current applications and characteristics of these structures, development directions for auxetic meta-materials were highlighted to meet future engineering demands for multi-functionality.
... A number of publications on these metamaterials introduce modifications to their structure. These include building composite systems [18][19][20][21][22] or hierarchical systems [10,[23][24][25][26] or modifying the connections of the rotating polygons [21,27]. A distinct portion of research concerns the fabrication of rotating polygon structures by cutting out rhombuses from selected materials (perforated plate): polymer [12,28,29] and textiles [30]. ...
The subject of the work is analysis, which presents a renowned auxetic structure based on so-called rotating polygons, which has been subject to modification. This modification entails introducing pivot points on unit cell surfaces near rectangle corners. This innovative system reveals previously unexplored correlations between Poisson’s ratio, the ratio of rectangle side lengths, pivot point placement, and structural opening. Formulas have been derived using geometric relationships to compute the structure’s linear dimensions and Poisson’s ratio. The obtained findings suggest that Poisson’s ratio is intricately tied to the structure’s opening degree, varying as the structure undergoes stretching. Notably, there are critical parameter limits beyond which Poisson’s ratio turns positive, leading to the loss of auxetic properties. For elongated rectangles, extremely high negative Poisson’s ratio values are obtained, but only for small opening angles, while with further stretching, the structure loses its auxetic properties. This observed trend is consistent across a broad category of structures comprised of rotating rectangles.
... This hierarchical metamaterial can possess NPR and large soft deformation behavior as well. In contrast to the multi-step pathways, some hierarchical auxetic metamaterials can be designed to generate synchronized deformation [169,170]. Seifi et al. [169] proposed 2D and 3D hierarchical structures with uniform and easily-controllable deformations using rotate-and-mirror operation, and the synchronized deformation was controlled by the synchronized motion of rotating units comprising the hierarchical structure. ...
Auxetic mechanical metamaterials are artificially architected materials that possess negative Poisson’s ratio, demonstrating transversal contracting deformation under external vertical compression loading. Their physical properties are mainly determined by spatial topological configurations. Traditionally, classical auxetic mechanical metamaterials exhibit relatively lower mechanical stiffness, compared to classic stretching dominated architectures. Nevertheless, in recent years, several novel auxetic mechanical metamaterials with high stiffness have been designed and proposed for energy absorption, load-bearing, and thermal-mechanical coupling applications. In this paper, mechanical design methods for designing auxetic structures with soft and stiff mechanical behavior are summarized and classified. For soft auxetic mechanical metamaterials, classic methods, such as using soft basic material, hierarchical design, tensile braided design, and curved ribs, are proposed. In comparison, for stiff auxetic mechanical metamaterials, design schemes, such as hard base material, hierarchical design, composite design, and adding additional load-bearing ribs, are proposed. Multi-functional applications of soft and stiff auxetic mechanical metamaterials are then reviewed. We hope this study could provide some guidelines for designing programmed auxetics with specified mechanical stiffness and deformation abilities according to demand.
... Several recent developments of Resch's interconnected assemblies considered 'hierarchical' generalisations of these structures 45,75,80,[82][83][84][85][86][87][88] . In hierarchical structures/materials, a distinct structural pattern repeats in different scales 89 , that is why they are also called 'multiscale' structures/materials 7 . ...
Mechanical metamaterials are man-made structures capable of achieving different intended mechanical properties through their artificial, structural design. Specifically, metamaterials with negative Poisson’s ratio, known as auxetics, have been of widespread interest to scientists. It is well-known that some pivotally interconnected polygons exhibit auxetic behaviour. While some hierarchical variations of these structures have been proposed, generalising such structures presents various complexities depending on the initial configuration of their basic module. Here, we report the development of pivotally interconnected polygons based on even-numbered modules, which, in contrast to odd-numbered ones, are not straightforward to generalize. Particularly, we propose a design method for such assemblies based on the selective removal of rotational hinges, resulting in fully-deployable structures, not achievable with previously known methods. Analytical and numerical analyses are performed to evaluate Poisson’s ratio, verified by prototyping and experimentation. We anticipate this work to be a starting point for the further development of such metamaterials.
... Elastic properties of these fractal structures could be derived using the iterative averaging approach (Novikov et al., 2001). Recently, hierarchical design of the rotating rigid structures brings rich mechanical properties, such as, control the extent of auxeticity (Gatt et al., 2015), strength enhancement (Tang et al., 2015), increased toughness (Sun and Pugno, 2013), increased versatility and tunability (Dudek et al., 2017), and synchronized deformations (Seifi et al., 2017;Lu et al., 2018). Generally, auxetic materials composed of ligaments (Prall and Lakes, 1997) or ribs (Lakes and Wojciechowski, 2008) were very light. ...
A novel two-dimensional (2D) mechanical metamaterial with highly programmable mechanical response under compressive load is presented in this paper by introducing hierarchical rotating structures, in which flexible structures are used to replace the rigid part in conventional rotating rigid structures. Multi-step deformation pathways and negative Poisson’s ratio were observed in in situ compression experiments and finite element simulations, suggesting that the mechanical behavior of the hierarchical metastructure is highly ordered and can be programmed by constraining angles of the proposed metamaterial. This work offers new insights to create mechanical metamaterial using hierarchical rotating structures for flexible devices and crashworthiness applications.
... In this paper, we show that rigid origami can construct this structure. Parallelogram linkages are planar 4-bar linkages in the shape of a parallelogram [4]. Extending the links outwards creates a structure, as shown in Figure 2, that is similar to a scissor-like structure. ...
Scissor-like structures are commonly composed of two straight rigid supports in a crisscross pattern connected by a pivot at its point of intersection [1]. Opposite angles formed by the supports are equal regardless of the structure’s folded state. Parallelogram linkages have a similar property. Rigid origami can be used to create these structures by combining two identical copies of a 4-crease single-vertex flat-foldable rigid origami, a single 4C, to form a flat-foldable composite structure, a double 4C. In this paper, we prove mathematically that regardless of the folded state of a single-4C, its even dihedral angles are equal, and odd dihedral angles are equal. As a result, the double 4C consists of 2 scissor-like structures. A past method to prove these dihedral angle equalities requires a more complex approach involving rotation matrices using Denavit and Hartenberg parameters [2,3]. This paper will provide a more intuitive method that proves the same equalities. We will also show that a similar construction of the double 4C using thick-panel versions of the single 4C satisfies the same dihedral angle equalities necessary for the formation of parallelogram linkages. The construction of the double 4C can help design self-folding mechanisms and useful metamaterials.
... kirigami-based structures [7,19,23], fractal hierarchical structures [54,55], and dimpled elastic sheets [52], have been implemented in designing multifunctional materials. However, microstructures with corrugated configuration have been overlooked, which may improve mechanical performance such as stretchability of associated metamaterials [56][57][58]. ...
Metamaterials, rationally designed multiscale composite systems, have attracted extensive interest for their potential applications in a broad range of applications due to their unique properties such as negative Poisson’s ratio,...
Kirigami—the Japanese art of cutting paper—has recently inspired the design of highly stretchable and morphable mechanical metamaterials that can be easily realized by embedding an array of cuts into a sheet. This study focuses on thin plastic sheets perforated with a hierarchical pattern of cuts arranged to form an array of hinged squares. It is shown that by tuning the geometric parameters of this hierarchy as well as thickness and material response of the sheets not only a variety of different buckling‐induced 3D deformation patterns can be triggered, but also the stress–strain response of the surface can be effectively programmed. Finally, it is shown that when multiple hierarchical patterns are brought together to create one combined heterogeneous surface, the mechanical response can be further tuned and information can be encrypted into and read out via the applied mechanical deformation. The mechanical response of kirigami thin sheets with a hierarchical pattern of cuts arranged to form an array of hinged squares is investigated. The combined experimental and numerical results indicate that by tuning the geometric parameters of this hierarchy not only a variety of different buckling‐induced 3D deformation patterns can be triggered, but also the stress–strain response of the surface can be effectively programmed.
A common spinning toy, called “buzzer”, consists of a perforated disk and flexible threads. Despite of its simple construction, a buzzer can effectively transfer translational motions into high-speed rotations. In the present work, we find that the disk can be spun by hand at an extremely high rotational speed, e.g., 200,000 rpm, which is much faster than the previously reported speed of any manually operated device. We explore, both experimentally and theoretically, the detailed mechanics and potential applications of such a thread–disk system. The theoretical prediction, validated by experimental measurements, can help design and optimize the system for, e.g., easier operation and faster rotation. Furthermore, we investigate the synchronized motion of multiple disks spinning on a string. Distinctly different twist waves can be realized by the multi-disk system, which could be exploited in the control of mechanical waves. Finally, we develop two types of manually-powered electric generators based on the thread–disk system. The high-speed rotation of the rotors enables a pulsed high current, which holds great promise for potential applications in, for instance, generating electricity and harvesting energy from ocean waves and other rhythmic translational motions.
The beam steering mechanism has been a key element for various applications ranging from sensing and imaging to solar tracking systems. However, conventional beam steering systems are bulky and complex and present significant challenges for scaling up. This work introduces the use of soft deployable reflectors combining a soft deployable structure with simple kirigami/origami reflective films. This structure can be used as a macroscale beam steering mechanism that is both simple and compact. This work first develops a soft deployable structure that is easily scalable by patterning of soft linear actuators. This soft deployable structure is capable of increasing its height several folds by expanding in a continuous and controllable manner, which can be used as a frame to deform the linearly stretchable kirigami/origami structures integrated into the structure. Experiments on the reflective capability of the reflectors are conducted and show a good fit to the modeling results. The proposed principles for deployment and for beam steering can be used to realize novel active beam steering devices, highlighting the use of soft robotic principles to produce scalable morphing structures.
Optical tracking is often combined with conventional flat panel solar cells to maximize electrical power generation over the course of a day. However, conventional trackers are complex and often require costly and cumbersome structural components to support system weight. Here we use kirigami (the art of paper cutting) to realize novel solar cells where tracking is integral to the structure at the substrate level. Specifically, an elegant cut pattern is made in thin-film gallium arsenide solar cells, which are then stretched to produce an array of tilted surface elements which can be controlled to within ±1°. We analyze the combined optical and mechanical properties of the tracking system, and demonstrate a mechanically robust system with optical tracking efficiencies matching conventional trackers. This design suggests a pathway towards enabling new applications for solar tracking, as well as inspiring a broader range of optoelectronic and mechanical devices.
We have produced stretchable lithium-ion batteries (LIBs) using the concept of kirigami, i.e., a combination of folding and cutting. The designated kirigami patterns have been discovered and implemented to achieve great stretchability (over 150%) to LIBs that are produced by standardized battery manufacturing. It is shown that fracture due to cutting and folding is suppressed by plastic rolling, which provides kirigami LIBs excellent electrochemical and mechanical characteristics. The kirigami LIBs have demonstrated the capability to be integrated and power a smart watch, which may disruptively impact the field of wearable electronics by offering extra physical and functionality design spaces.
Hard and soft structural composites found in biology provide inspiration for the design of advanced synthetic materials. Many examples of bio-inspired hard materials can be found in the literature; far less attention has been devoted to soft systems. Here we introduce deterministic routes to low-modulus thin film materials with stress/strain responses that can be tailored precisely to match the non-linear properties of biological tissues, with application opportunities that range from soft biomedical devices to constructs for tissue engineering. The approach combines a low-modulus matrix with an open, stretchable network as a structural reinforcement that can yield classes of composites with a wide range of desired mechanical responses, including anisotropic, spatially heterogeneous, hierarchical and self-similar designs. Demonstrative application examples in thin, skin-mounted electrophysiological sensors with mechanics precisely matched to the human epidermis and in soft, hydrogel-based vehicles for triggered drug release suggest their broad potential uses in biomedical devices.
Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poisson's ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poisson's ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts. H ierarchical materials and structures are a class of systems which are composed of structural elements which themselves have structure 1. These naturally occurring or man-made systems benefit from significantly enhanced mechanical properties 1,2 such as lightweight high-strength characteristics and an increased resistance to crack propagation 2. These qualities are needed by biological structures like bones 3 , wood 4
Dilational materials are stable three-dimensional isotropic auxetics with an
ultimate Poisson's ratio of -1. We design, evaluate, fabricate, and
characterize crystalline metamaterials approaching this ideal. To reveal all
modes, we calculate the phonon band structures. On this basis, using cubic
symmetry, we can unambiguously retrieve all different non-zero elements of the
rank-4 effective metamaterial elasticity tensor, from which all effective
elastic metamaterial properties follow. While the elastic properties and the
phase velocity remain anisotropic, the effective Poisson's ratio indeed becomes
isotropic and approaches -1 in the limit of small internal connections. This
finding is also supported by independent static continuum-mechanics
calculations. In static experiments on macroscopic polymer structures
fabricated by three-dimensional printing, we measure Poisson's ratios as low as
-0.8 in good agreement with theory. Microscopic samples are also presented.
In this paper, a new kind of hierarchical tube with a negative Poisson’s ratio (NPR) is proposed. The first level tube is constructed by rolling up an auxetic hexagonal honeycomb. Then, the second level tube is produced by substituting the arm of the auxetic sheet with the first level tube and rolling it up. The Nth ( N ≥ 1 ) level tube can be built recursively. Based on the Euler beam theory, the equivalent elastic parameters of the NPR hierarchical tubes under small deformations are derived. Under longitudinal axial tension, instead of shrinking, all levels of the NPR hierarchical tubes expand in the transverse direction. Using these kinds of auxetic tubes as reinforced fibers in composite materials would result in a higher resistance to fiber pullout. Thus, this paper provides a new strategy for the design of fiber reinforced hierarchical bio-inspired composites with a superior pull-out mechanism, strength and toughness. An application with super carbon nanotubes concludes the paper.
We investigated the mechanical behavior of two-dimensional hierarchical honeycomb structures using analytical, numerical and experimental methods. Hierarchical honeycombs were constructed by replacing every three-edge vertex of a regular hexagonal lattice with a smaller hexagon. Repeating this process builds a fractal-appearing structure. The resulting isotropic in-plane elastic properties (effective elastic modulus and Poisson’s ratio) of this structure are controlled by the dimension ratios for different hierarchical orders. Hierarchical honeycombs of first and second order can be up to 2.0 and 3.5 times stiffer than regular honeycomb at the same mass (i.e., same overall average density). The Poisson’s ratio varies from nearly 1.0 (when planar ‘bulk’ modulus is considerably greater than Young’s modulus, so the structure acts ‘incompressible’ for most loadings) to 0.28, depending on the dimension ratios. The work provides insight into the role of structural organization and hierarchy in regulating the mechanical behavior of materials, and new opportunities for developing low-weight cellular structures with tailorable properties.
The transverse compression and shear collapse mechanisms of a second order hierarchical corrugated truss structure have been analyzed. The two competing collapse modes of a first order corrugated truss are elastic buckling or plastic yielding of the truss members. In second order trusses, elastic buckling and yielding of the larger and smaller struts, shear buckling of the larger struts, and wrinkling of the face sheets of the larger struts have been identified as the six competing modes of failure. Analytical expressions for the compressive and shear collapse strengths in each of these modes are derived and used to construct collapse mechanism maps for second order trusses. The maps are useful for selecting the geometries of second order trusses that maximize the collapse strength for a given mass. The optimization reveals that second order trusses made from structural alloys have significantly higher compressive and shear collapse strengths than their equivalent mass first order counterparts for relative densities less than about 5%. A simple sheet metal folding and dip brazing method of fabrication has been used to manufacture a prototype second order truss with a relative density of about 2%. The experimental investigation confirmed the analytical strength predictions of the second order truss, and demonstrate that its strength is about ten times greater than that of a first order truss of the same relative density.
This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson's ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.
The role of structural hierarchy in determining bulk material properties is examined. Dense hierarchical materials are discussed, including composites and polycrystals, polymers, and biological materials. Hierarchical cellular materials are considered, including cellular solids and the prediction of strength and stiffness in hierarchical cellular materials.
The development of individual organs in animal embryos involves the formation of tissue-specific stem cells that sustain cell
renewal of their own tissue for the lifetime of the organism. Although details of their origin are not always known, tissue-specific
stem cells usually share the expression of key transcription factors with cells of the embryonic rudiment from which they
arise, and are probably in a similar developmental state. On the other hand, the isolation of pluripotent stem cells from
the postnatal organism has encouraged the formulation of models of embryonic and postnatal development that are at variance
with the conventional ones. Possible explanations for the existence of such cells, and the issue of whether they also exist
in vivo, are discussed.
Pump drill is an easily constructed ancient device that has been used for centuries to start fires and bore holes. It can effectively transfer rhythmic translational motions into vibratory, bi-directional rotary insertions. Here we explore, both experimentally and theoretically, the kinematics, dynamics, and potential applications of pump drills. The theoretical model, validated by experimental measurements, enables us to obtain the optimal structural geometries (e.g., the thread length and the crossbar span) of pump drills that maximize the mechanical responses such as the winding angle of the threads. Furthermore, the dependence of its rotational speed and piercing force on the loading conditions is investigated. Finally, manually powered devices, including an electric generator and a centrifugal separator, are developed based on the pump drill. This study paves a way towards promising applications of the pump drill in, for instance, energy harvesting and centrifugation.
In this paper we propose a general method for creating a new type of hierarchical structures at any level
in both 2D and 3D. A simple rule based on a rotate-and-mirror procedure is introduced to achieve multilevel
hierarchies. These new hierarchical structures have remarkably few degrees of freedom compared
to existing designs by other methods. More importantly, these structures exhibit synchronized motions
during opening or closure, resulting in uniform and easily-controllable deformations. Furthermore, a
simple analytical formula is found which can be used to avoid collision of units of the structure during
the closing process. The novel design concept is verified by mathematical analyses, computational
simulations and physical experiments.
We studied the mechanical response of a recently developed new class of mechanical metamaterials based on the paper art of cutting, kirigami. Specially, the geometrical and structural design of representative cut units, via a combined line cut, cut-out, and hierarchy of the structure, was explored for achieving both extreme stretchability and/or compressibility in kirigami metamaterials through experiments, alongside geometrical modeling and finite element simulations. The kirigami design was tested on constituent materials including non-stretchable copy papers and highly stretchable silicone rubber to explore the role of constituent material properties. The cut unit in the shape of solid rectangles with the square shape as a special case was demonstrated for achieving the extreme stretchability via rigid rotation of cut units. We found that compared to the square cut units, the theoretically predicted maximum stretchability via unit rotation in rectangle units (aspect ratio 2:1) increased dramatically from about 41% to 124% for the level 1 cut structure without hierarchy, and from about 62% to 156% for the level 2 hierarchical cut structure, which was validated by both experiments and simulations. To demonstrate the achievement of both extreme stretchability and compressibility, we replaced the solid square cut units with porous squares and re-entrant lattice shapes in silicone rubber based metamaterials. We found that a porous structure can enable an extreme compressibility of as high as 81%.
Applying hierarchical cuts to thin sheets of elastomer generates super-stretchable and reconfigurable metamaterials, exhibiting highly nonlinear stress-strain behaviors and tunable phononic bandgaps. The cut concept fails on brittle thin sheets due to severe stress concentration in the rotating hinges. By engineering the local hinge shapes and global hierarchical structure, cut-based reconfigurable metamaterials with largely enhanced strength are realized.
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.
Elastic instability of soft cellular solids plays an increasingly important role in the creation of metamaterials with smart properties. Inspiration for much of this research comes from a planar metamaterial with negative Poisson's ratio behavior induced by elastic instability. Here we extend the concept of buckling induced pattern switch further to the design of a new series of three-dimensional metamaterials with negative Poisson's ratio over a large strain range. The highlight of this work is that our designs are based on very simple initial geometric shapes.Different deformation patterns of materials without and with auxetic behavior.
Reconfigurable antennas, with the ability to radiate more than one pattern at different frequencies and polarizations, are necessary in modern telecommunication systems. The requirements for increased functionality (e.g., direction finding, beam steering, radar, control, and command) within a confined volume place a greater burden on today's transmitting and receiving systems. Reconfigurable antennas are a solution to this problem. This paper discusses the different reconfigurable components that can be used in an antenna to modify its structure and function. These reconfiguration techniques are either based on the integration of radio-frequency microelectromechanical systems (RF-MEMS), PIN diodes, varactors, photoconductive elements, or on the physical alteration of the antenna radiating structure, or on the use of smart materials such as ferrites and liquid crystals. Various activation mechanisms that can be used in each different reconfigurable implementation to achieve optimum performance are presented and discussed. Several examples of reconfigurable antennas for both terrestrial and space applications are highlighted, such as cognitive radio, multiple-input-multiple-output (MIMO) systems, and satellite communication.
Hierarchical lattices are made of finer lattices in successive smaller scales. This paper analytically studies the effect of hierarchy on the stiffness and strength of self-similar and hybrid type lattices, made by combining two distinct variants of topologies, governed by the bending and stretching dominated architectures. Scaling argument and physical reasoning are used to explain the behaviour of these lattices. The results show that the in-plane stiffness and the elastic buckling strength of the bending-bending lattices progressively improve with hierarchy; in contrast, only the buckling strength improves substantially for the stretching-stretching lattices, while the stiffness decreases. Low density bending-stretching lattices are unique with a significant improvement in stiffness, buckling, plastic collapse or crushing strength with hierarchy, whereas the stretching-bending lattices exhibit flexibility with lower strength. Despite no gain in stiffness, substantial gain in out-of-plane compressive strength is obtained with hierarchy because of the enhanced elastic and plastic buckling strength. Thus the advantage of combining lattices at multiple length scales provides a wide spectrum of choices for tailoring the properties for target applications including high performance core material, energy absorption or packaging.
Hierarchical structures are predicted to have ultra-light weight and superior mechanical properties, including excellent anti-buckling ability and energy absorption capability. Based on the improvement of making technology, hierarchical composite honeycombs (HCHs) have been designed, made and tested. With woven textile sandwich walls, the HCH is ultra-light and renders relatively ideal complete stress–strain curve with a stable displacement plateau at a relative high stress level in compression. A plastic model was suggested based on tested failure maps to reveal the plastic deformation and energy absorbing mechanism of the HCH. The plastic model well fitted the tested curves and defines a lower limit of the plastic deformation curve.
Precision thermometry of the skin can, together with other measurements, provide clinically relevant information about cardiovascular health, cognitive state, malignancy and many other important aspects of human physiology. Here, we introduce an ultrathin, compliant skin-like sensor/actuator technology that can pliably laminate onto the epidermis to provide continuous, accurate thermal characterizations that are unavailable with other methods. Examples include non-invasive spatial mapping of skin temperature with millikelvin precision, and simultaneous quantitative assessment of tissue thermal conductivity. Such devices can also be implemented in ways that reveal the time-dynamic influence of blood flow and perfusion on these properties. Experimental and theoretical studies establish the underlying principles of operation, and define engineering guidelines for device design. Evaluation of subtle variations in skin temperature associated with mental activity, physical stimulation and vasoconstriction/dilation along with accurate determination of skin hydration through measurements of thermal conductivity represent some important operational examples.
A 3D hierarchical computational model of deformation and stiffness of wood, which takes into account the structures of wood at several scale levels (cellularity, multilayered nature of cell walls, composite-like structures of the wall layers) is developed. At the mesoscale, the softwood cell is presented as a 3D hexagon-shape-tube with multilayered walls. The layers in the softwood cell are considered as considered as composite reinforced by microfibrils (celluloses). The elastic properties of the layers are determined with Halpin–Tsai equations, and introduced into mesoscale finite element cellular model. With the use of the developed hierarchical model, the influence of the microstructure, including microfibril angles (MFAs, which characterizes the orientation of the cellulose fibrils with respect to the cell axis), the thickness of the cell wall, the shape of the cell cross-section and the cell dimension (wood density), on the elastic properties of softwood was studied.
Buckling-induced reversible symmetry breaking and amplification of chirality using macro- and microscale supported cellular structures is described. Guided by extensive theoretical analysis, cellular structures are rationally designed, in which buckling induces a reversible switching between achiral and chiral configurations. Additionally, it is demonstrated that the proposed mechanism can be generalized over a wide range of length scales, geometries, materials, and stimuli.
Conceptual hardware architecture of skin-like circuits is described. An elastomeric skin carries rigid islands on which active subcircuits are made. The subcircuit islands are interconnected by stretchable metallization. We concentrate on recent advances in stretchable thin-film conductors, by covering their construction, evaluation, and laboratory and theoretical analysis. Reversibly stretchable conductors with electrically-critical strains ranging from 10% to 100% have been made. r 2004 Elsevier B.V. All rights reserved.
A new mechanism to achieve a negative Poisson's ratio is presented. An arrangement is made which involves rigid squares connected together at their vertices by hinges. The off-axis mechanical properties obtained from the standard transformation equations show that the idealized system is isotropic. The Poisson's ratio has a value of -1 irrespective of the direction of loading. The geometry modelled is the projection of a plane in inorganic crystalline materials and involves octahedrally co-ordinated atoms.
Soft cellular structures that comprise a solid matrix with a square array of holes open avenues for the design of novel soft and foldable structures. Our results demonstrate that by simply changing the shape of the holes the response of porous structure can be easily tuned and soft structures with optimal compaction can be designed.
Materials with negative Poisson's ratios (auxetic) get fatter when stretched and thinner when compressed. This paper discusses a new explanation for achieving auxetic behaviour in foam cellular materials, namely a ‘rotation of rigid units’ mechanism. Such auxetic cellular materials can be produced from conventional open-cell cellular materials if the ribs of cell are slightly thicker in the proximity of the joints when compared to the centre of the ribs with the consequence that if the conventional cellular material is volumetrically compressed (and then ‘frozen’ in the compressed conformation), the cellular structure will deform in such a way which conserves the geometry at the joints (i.e. behave like ‘rigid units’) whilst the major deformations will occur along the length of the more flexible ribs which form ‘kinks’ at their centres as a result of the extensive buckling. It is proposed that uniaxial tensile loading of such cellular systems will result auxetic behaviour due to re-unfolding of these ‘kinks’ and re-rotation of the ‘rigid joints’.
Two-dimensional (2D) hierarchical cellular materials made up of sandwich walls are predicted to have superior mechanical properties compared with solid-wall cellular materials. Equations of the stiffness, the buckling strength, the plastic collapse strength, the brittle failure strength and the fracture toughness were deduced. The enhancement of the mechanical properties of 2nd order hierarchical honeycombs is substantial (even an order of magnitude). The hierarchical honeycomb is much more damage tolerant and insensitive to wavy imperfections of the cell wall. Sandwich struts also enhance the buckling strength of the stretching-dominated 2nd order lattice grid material. Made up of sandwich struts, the hierarchical honeycomb has comparable mechanical properties with the stretching-dominated lattice grid material.
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