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Programmable stiffness and shape modulation in origami materials: Emergence of a distant actuation feature
Supplementary resource (1)
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June 2020
... Mechanical metamaterials are artificially engineered microstructures where the effective properties can be obtained through a conducive nexus among intrinsic material properties, geometry and mechanics, leading to extreme, tunable and multifunctional mechanical behavior which are not normally achievable in naturally-occurring materials. Over the last decade or so, mechanical metamaterials [1,2] have indubitably demonstrated unprecedented abilities in terms of specific stiffness [3,4,5], auxeticity [6], impact resistance [7,8], energy absorption [9,10], energy harvesting [11,12], fracture toughness [13,14], variable permeability [15], wave propagation and modulation [16,17,18], shape trans-formation [19], critical properties concerning sensors and actuators [20,21], and structural designs with better stress distribution and deformation resistance. This has led to an accelerated adoption of such architected materials in technologically demanding sectors such as aerospace, biomedical, mechanical, and civil for achieving extreme or tunable mechanical properties with multi-objective, and often conflicting demands. ...
... While a wide range of effective material properties can be achieved in such passive material microstructures, the properties cannot be tuned in an on-demand basis after they are manufactured. The recent developments in this direction include bi-level topology architected optimum metamaterials [5], hierarchical metamaterials [24], disordered metamaterials [25], anti-curvature metamaterils with programmed curvature [26,27,28,29], multi-material and space-filled lattices [30,31], origami and kirigami-inspired metamaterials [32,19], to mention a few. Recently the concept of pneumatic elastostatics and deployability in mechanical metamaterials has been proposed based on inflatable lattices that can exhibit extreme specific stiffness along with on-demand tunability [33]. ...
... Keeping the voltage, V as constant, we take the variational of the summation of the total potential energy in Equation 3 and the internal energy in the piezoelectric layer. Then we get Equation 19. ...
Owing to the architected void-filled low-density configurations, metamaterials are prone to defects during the complex manufacturing process, or damages under operational conditions. Recently mechanical cloaking has been proposed to shield the effect of such disorders in terms of homogenized mechanical responses. The major drawback in these studies are that the damage location should be known a priori, and the cloak is designed around that damaged zone before manufacturing. Such postulation does not allow unsupervised damage resilience during the manufacturing and service life of metamaterials by active reconfiguration of the stress field depending on the random and unpredictable evolution of damage. Here, we propose a radically different approach by introducing piezoelectric lattices where the effect of random appearance of any single or multiple disorders and damages with complex shapes, sizes and distributions can be shielded through active multi-physically controlled cloaks by voltage-dependent modulation of the stress fields within the cloaking region. Notably, this can be achieved without breaking periodicity and any additional material in the cloaking region unlike earlier studies concerning mechanical cloaks. The proposed active class of elastic metamaterials will bring a step-change in the on-demand mechanical performance of critically important structural components and unsupervised damage resilience for enhanced durability and sustainability.
This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 1)’.
... These metamaterials can be both rigid and deformable (refer to Figure 5(F)(a-f )). The subsequent classication of origami metamaterials can be based on dierent patterns such as Miura [148], assembled Miura [149], waterbomb [32], eggbox [150,151], kresling [152], square-twist [153] and dierent other multi-DOF rigid origami [154]. The rigid hybrid ori/kirigami can be cut-and-fold [155] and assembled to obtain new architectures [156]. ...
... A recent study proposes kirigami-inspired modular metamaterials for contact-induced stiness modulation and programming of constitutive laws [31]. It is further shown that mixed-mode multi-directional auxeticity (including the transition from a non-auxetic to auxetic behavior, and viceversa) and programmable stiness can be achieved through origami and kirigami-inspired metamaterials without external non-mechanical stimuli [31,105,32] . i.e., the rationally designed mechanical metamaterials can show ultra-high stiness, high toughness, high strength and at the same time can have low mass density [228,229]. ...
... (d) Micro-structure and far-eld actuation dependent shape morphing. (e) Microstructure-dependent programming of constitutive relationship[32]. ...
Mechanical metamaterials are engineered materials with unconventional mechanical behavior that originates from artificially programmed microstructures along with intrinsic material properties. With tremendous advancement in computational and manufacturing capabilities to realize complex microstructures over the last decade, the field of mechanical metamaterials has been attracting wide attention due to immense possibilities of achieving unprecedented multi-physical properties which are not attainable in naturally-occurring materials. One of the rapidly emerging trends in this field is to couple the mechanics of material behavior and the unit cell architecture with different other multi-physical aspects such as electrical or magnetic fields, and stimuli like temperature, light or chemical reactions to expand the scope of actively programming on-demand mechanical responses. In this article, we aim to abridge outcomes of the relevant literature concerning mechanical and multi-physical property modulation of metamaterials focusing on the emerging trend of bi-level design, and subsequently highlight the broad-spectrum potential of mechanical metamaterials in their critical engineering applications. The evolving trends, challenges and future roadmaps have been critically analyzed here involving the notions of real-time reconfigurability and functionality programming, 4D printing, nano-scale metamaterials, artificial intelligence and machine learning, multi-physical origami/kirigami, living matter, soft and conformal metamaterials, manufacturing complex microstructures, service-life effects and scalability.
... Left figure from Ref. [143]. References [43], [62], [63], and [145][146][147][148][149][150][151][152][153][154][155][156][157]. Left figure from Ref. [63]. ...
... The bar and hinge model has become a widely used reduced-order mechanical model for representing origami systems [28,62,151,152]. The model is sometimes referred to as the truss-based mechanism model [149,150,155] or the pin-jointed bar framework [61], but here, will use the name bar and hinge model because it is an expressive name (directly pointing to the two elements involved). ...
... where E i is the Young's modulus, A i is the bar area, x 1 and x 2 are the nodal coordinates, and l 0;i is the original length of the bar. Many studies use this linear elastic bar formulation because it is simple and easy to derive [43,136,149,150,152,156]. More advanced hyper-elastic formulations are also available for deriving the total potential of the bar element [63,192,193]. ...
Origami-inspired systems are attractive for creating structures and devices with tunable properties, multiple functionalities, high-ratio packaging capabilities, easy fabrication, and many other advantageous properties. Over the past decades, the community has created a variety of simulation techniques to analyze the kinematic motions, mechanical properties, and multi-physical characteristics of origami systems. These various simulation techniques are formulated with different assumptions and are often tailored to specific origami designs, and thus, it is valuable to systematically review the state-of-the-art of origami simulation techniques. This review presents the formulations of different origami simulations, analyzes their strengths and weaknesses, and discusses the potential application scenarios of different simulation techniques. The three major types of simulations: kinematics-based simulations, mechanics-based simulations, and multi-physics based simulations are all discussed in this work. The paper also addresses how to select appropriate simulation techniques for studying different origami-inspired systems and the potential future challenges in the field of origami simulation.
... 1(a)-1(c)]. Although the waterbomb tube or the waterbomb tessellation is instances of the most studied origami pattern [31][32][33][34][35][36][37], no work considers the general kinematics of the waterbomb tube without any symmetry assumptions. In this paper, we capture the complex nature of the waterbomb tube as a multi-DOF 1D Maxwell lattice using a discrete dynamical system model [37][38][39][40][41][42]. ...
... multipliers necessarily include a conjugate pair of complex multipliers with multiplicity 1 whose magnitude is equal to 1. The 2-bDOF induced by them corresponds to the Nfold-symmetric undulation reported in the previous research [34,37,41,52]. In the finite deformation, by transitioning the orbits corresponding to a family of quasiperiodic solutions, we can tune the "amplitude" and "phase" of the N-foldsymmetric mode independently [37,41]. ...
Maxwell lattices are periodic frameworks characterized by a balance between the number of kinematic variables and constraints in each unit cell, attracting attention as a source of topological mechanical metamaterials. In particular, one-dimensional (1D) Maxwell lattices maintain a constant number of degrees of freedom (DOFs) as the number of unit cells increases, offering advantages in the design and control of their kinematics. Here, we construct a 1D Maxwell lattice with tunable DOFs, termed the Maxwell origami tube, by closing a triangulated origami tessellation, which is a 2D Maxwell lattice. In topological mechanics, the infinitesimal deformation modes of uniformly configured Maxwell lattices are classified into edge and bulk modes. Unlike conventional 1-DOF 1D Maxwell lattices, multi-DOF 1D Maxwell lattices exhibit a mixture of DOFs corresponding to edge and bulk modes, which we term eDOFs and bDOFs. This paper investigates how the eDOFs and bDOFs of the Maxwell origami tube depend on the crease patterns and folded states using a discrete dynamical system model. We find that ground states with zero and nonzero bDOFs can coexist within a single crease pattern. Additionally, in states with nonzero bDOF, the ratio of bDOF to total DOF decreases as the total DOF increases. In contrast, we present another origami tube with a constant DOF of 2, which represents the first overconstrained lattice to exhibit nonuniform bulk modes. This work highlights the versatility of Maxwell lattices and provides a theoretical foundation for designing novel mechanical metamaterials.
Published by the American Physical Society 2025
... Nowadays origami-based methods have received prominence among engineering and science researchers as a new way to develop programmable metastructures and metamaterials [1,2,3,4,5,6,7,8]. The generation of creases following a periodic pattern makes connected unit cells to develop mechanical metamaterials for rich multi-functional applications 1 Email address: alok_kt@me.iitr.ac.in (AKT), sanjay.upadhyay@me.iitr.ac.in (SHU), t.mukhopadhyay@soton.ac.uk (TM) [9,10]. The origami metamaterials can be furnished with incomparable and even unconventional mechanical properties attributable to complex interactions between constituent sheet deformations and folding behavior along with nonlinearities arising from multiple sources [11,12,13,14]. ...
... This term is essential for describing the transition between two stable states (bistability). Following the Dung method, we substitute the following parts into equation 7 along with the time derivativesu h andü h u h (t) =ũ c cos (Ωt) +ũ s sin (Ωt) (8) u h (t) =−u c Ω sin (Ωt) +ũ s Ω cos (Ωt) (9) u h (t) =−u c Ω 2 cos (Ωt) −ũ s Ω 2 sin (Ωt) (10) After expanding the nonlinear cubic term, cos(Ωt) and sin(Ωt), considering the frequency term Ω and neglecting other coecient terms of frequency, followed by arranging Fourier coecient to zero, we get ...
Kresling origami-based metamaterials have gained significant attention lately due to their mechanical advantages like deployability, energy manipulation and absorption, vibration control and tailorable constitutive behavior. While previous investigations have primarily focused on kinematics and statics, as most engineering applications experience dynamic conditions, few recent studies have examined the dynamic performance including transient and linear vibration. In this paper, we computationally investigate the nonlinear dynamics of Kresling origami in an expanded design space through the introduction of conical architecture. The conical Kresling origami module (CKOM) leads to a highly nonlinear behavior, originating from the geometrical constraints. This makes the dynamic behavior under specific natures of external disturbance more complex and chaotic, while programmable as a function of the geometrical features. CKOM provides an excellent support system and better stability at period-n attractor, which means that the system behaves in the same pattern after n-period of oscillation. It is further noted that the CKOM system is an elastically foldable truss-like idealized structure, which often exhibits interesting static behavior like bi-stability. Programmability in the expanded design space of conicity and other geometrical parametric features of the Kresling tubular origami would lead to widespread applications including spacecraft, aircraft wings, robotics, vehicles, and various deployable structures across the length scales.
... Accordingly, by integrating a low coefficient of thermal expansion (CTE) and Poisson's ratio (PR) into the cylindrical metastructures will provide a high dimensional stability, so as to guarantee the high accuracy of the components and structures. However, to date, the literature reported cylindrical metastructures always focus on achieving the lightweight [11], high strength [12] and stiffness [13], excellent energy absorption [14], as well as single programmability of either PR [15] or CTE [16]. It obviously fails to meet the emerging demand for multi-functional integration of low CTE and PR. ...
... As previously mentioned, the existing studies [15,16] mainly focus on achieving sole programmable CTE or PR. Comparatively, the designed cylindrical metastructures here simultaneously integrate the low CTE and programmable PR functions, providing a candidate for both mechanical-and temperature-sensitive components. ...
Multi-functional cylindrical metastructures, integrating the controllability in both coefficient of thermal expansion (CTE) and Poisson’s ratio (PR), provide promising alternatives for both temperature- and mechanical-sensitive components used in advanced industrial equipment. However, the sophisticated cellular and cylindrical geometries still give rise to an enormous challenge in fabrication process, and hence the controllability in both CTE and PR is still not practically realised. Herein, a series of new multi-functional cylindrical metastructures are designed by a curling strategy to exclusively integrate the controllability in both CTE and PR. Besides, the laser powder bed fusion (PBF-LB) process is originally developed to fabricate the cylindrical metastructures by using Invar 36 alloy as the constituent, and the exceptional manufacturing quality is realised by the customised PBF-LB process. In addition, the cylindrical metastructures effectively inherit the Invar effect of the constituent, and the controllable low CTEs, in the range of 1.80∼1.90 ppm/°C, are first experimentally achieved. Furthermore, the PR is also flexibly and experimentally controlled in the range of -0.62∼+0.43. These cylindrical metastructures open the avenue towards the cooperative design and additive manufacturing of multi-functional metastructures, which integrate lightweight, preferred mechanical performances or functions, motivated by the urgent requirement from advanced industrial equipment.
... Static mechanical properties, e.g., superior shock-absorption performance [18], superstrength [19], ultrahigh stretchability [20], negative Poisson's ratio [21], negative stiffness [22]. Dynamic mechanical properties [23] such as programmable deformation [24], programmable Poisson's ratio [25], programmable coefficient of thermal expansion [26], programmable stiffness [27], and programmable energy absorption [24][25][26][27][28]. In addition, mechanical metamaterials can also be classified as origami metamaterials [29], investigate the tunable two-step deformation, tunable stiffness, tunable energy absorption, and programmable properties of 2D metamaterials (constructed by UC A and UC B , respectively). ...
... Static mechanical properties, e.g., superior shock-absorption performance [18], superstrength [19], ultrahigh stretchability [20], negative Poisson's ratio [21], negative stiffness [22]. Dynamic mechanical properties [23] such as programmable deformation [24], programmable Poisson's ratio [25], programmable coefficient of thermal expansion [26], programmable stiffness [27], and programmable energy absorption [24][25][26][27][28]. In addition, mechanical metamaterials can also be classified as origami metamaterials [29], investigate the tunable two-step deformation, tunable stiffness, tunable energy absorption, and programmable properties of 2D metamaterials (constructed by UC A and UC B , respectively). ...
Mechanical metamaterials have attracted much attention in recent years because of excellent properties. However, most mechanical metamaterials have only a relatively fixed and single deformation mode. Although some multi-step deformation metamaterials have been proposed, their rich static and dynamic mechanical properties have yet to be studied in depth. Therefore, a lattice-mechanical metamaterial is introduced in this study. Under vertical compression, different unit cells under the same architecture can achieve two or three steps of deformation, respectively. Metamaterials built from these unit cells can also achieve the same properties. These properties can exist in multiple directions and are not affected by the number of unit cells. In addition, this metamaterial not only has adjustable two-step deformation, adjustable stiffness, and adjustable energy absorption properties but it can also be spatially programmed by changing geometric parameters and tessellation. Finally, a 3D design version of the metamaterial is provided, and its conceptual application is briefly demonstrated. The developed metamaterial can achieve more static and dynamic mechanical properties while taking into account two-step deformation. This can provide richer content for the development of mechanical metamaterials and also provide new perspectives for the application of energy absorbers, aerospace, and industrial products.
... Articially engineered materials can achieve a wide range of tailor-made multifunctional abilities which may not always be available in naturally occurring materials [1]. Their micro-scale design can present unprecedented and unconventional, yet useful properties like ultra-lightweight characteristics [2,3], shape programming [2,4], crushing resistance and high specic energy absorption [5,6,7], auxetic properties [8,9,10,11,12], negative elastic moduli [13,14,15], meta-uid characteristics [16,17], negative mass density [18,19], tunable wave propagation characteristics [20], programmable constitutive laws [21], active mechanical property modulation [22,23], and many other multi-physical properties [24,25,26,27,28]. ...
... Articially engineered materials can achieve a wide range of tailor-made multifunctional abilities which may not always be available in naturally occurring materials [1]. Their micro-scale design can present unprecedented and unconventional, yet useful properties like ultra-lightweight characteristics [2,3], shape programming [2,4], crushing resistance and high specic energy absorption [5,6,7], auxetic properties [8,9,10,11,12], negative elastic moduli [13,14,15], meta-uid characteristics [16,17], negative mass density [18,19], tunable wave propagation characteristics [20], programmable constitutive laws [21], active mechanical property modulation [22,23], and many other multi-physical properties [24,25,26,27,28]. ...
As a consequence of intense investigation on possible topologies of periodic lattices, the limit of specific elastic moduli that can be achieved solely through unit cell-level geometries in artificially-engineered lattice-based materials has reached a point of saturation. There exists a robust rationale to involve more elementary-level mechanics for pushing such boundaries further to develop extreme lightweight multi-functional materials with adequate stiffness. We propose a novel class of inflatable lattice materials where the global-level stiffness can be derived based on a fundamentally different mechanics compared to conventional lattices having beam-like solid members, leading to extreme specific stiffness due to the presence of air in most of the lattice volume. Further, such inflatable lattices would add multi-functionality in terms of on-demand performances such as compact storing, portability and deployment along with active stiffness modulation as a function of air pressure. We have developed an efficient unit cell-based analytical approach therein to characterize the effective elastic properties including the effect of non-rigid joints. The proposed inflatable lattices would open new frontiers in engineered materials and structures that will find critical applications in a range of technologically demanding industries such as aircraft structures, defense, soft robotics, space technologies, biomedical and various other mechanical systems.
... As shown in Figure 13, Endogenous factor programming is mainly composed of geometric parameter programming and structural parameter programming. Geometric parameter programming refers to controlling the mechanical properties of metamaterials through the programming of geometric parameters [214]. For example, Overvelde et al. proposed a metamaterial constructed based on complex geometric extruded polyhedra unit cells, which can achieve programmable deformation properties through geometric parameters programming [202]. ...
... Origami Geometric parametric programming Stiffness [214,223], Poisson's ratio [224], Deformation [225], Multistability [226], Compressive modulus [191] Krigami Geometric parametric programming Deformation [168], Stiffness [227], Stress-strain curve [228], Hyperelasticity [229] Lattice Geometric parametric programming Poisson's ratio [230], Deformation [231], Stiffness [207], Energy absorption [232] Other Geometric parametric programming Poisson's ratio [193], Deformation [211] Geometric hierarchical structure programming Poisson's ratio [233], Deformation [203], Stiffness [234], Energy absorption [235] Substrate materials hierarchical programming Coefficient of thermal expansion [236], Poisson's ratio [209], Deformation [237] Table 6. Examples of programmable mechanical properties based on external driving forces. ...
Abstract
Interdisciplinary design thinking and methods are developed based on interdisciplinary research backgrounds. Through cross-integration with other disciplines, it can realize the design’s interdisciplinary collaborative innovation and development. At the same time, with the increasing interdisciplinary research interest in programmable mechanical metamaterials, design urgently needs to produce an interdisciplinary design thinking and method model to guide the development of related design research activities. Based on this, this research uses interdisciplinary research methods (mainly grafts method) to transplant the construction methods and related contents of programmable mechanical metamaterials into the research of design thinking and methods to propose a set of interdisciplinary design thinking based on programmable mechanical metamaterials (IDTPMMs). At the same time, under the guidance of IDTPMM, an interdisciplinary design method based on programmable mechanical metamaterials (IDMPMMs) is proposed. The thinking and method take the IDTPMM and IDMPMM process models as the concrete manifestation forms. Subsequently, this study selected two architecture design cases to analyze the rationality of IDTPMM and IDMPMM. This study believes that the proposal of IDTPMM and IDMPMM can narrow the focus of design research from the traditional macro scale to the micro scale of material research and development, which can drive design innovation with material innovation. Meanwhile, it can also change the design research from passive use of existing material mechanical properties to active programming control of material mechanical properties according to demand, which will greatly enhance the programmability, adjustability, controllability, and flexibility of design research with materials as carriers and objects. Additionally, this will have an essential impact on broadening the field of design interdisciplinary research and innovating design thinking and methods. In addition, IDTPMM and IDMPMM will also provide systematic theoretical guidance for designers to conduct interdisciplinary research on design a
... These metamaterials derive their unique characteristics not only from their intrinsic material properties but also from the geometric arrangement of constituent unit cells. As a result, it becomes possible to modify and fine-tune the material properties of these metamaterials according to the requirements of various applications, enabling the creation of innovative materials with distinct functionalities [7,8,9,10,11,12]. Due to their exceptional specific stiffness, strength and energy absorption capability, lightweight metamaterials find extensive applications in various engineering fields [13,14,15,16,17]. ...
Functionally graded materials can exhibit remarkable tolerance towards extreme hot or cold environments and chemical surface degradation. This article exploits such properties of functionally graded materials to propose a new class of transversely curved metamaterial architectures with high specific stiffness for operations under extreme surrounding conditions. We envisage the next-generation concept design of hydrogen storage tanks with functionally graded metamaterial core for aerospace and automotive applications. Based on such innovative lattice metamaterial based design of hydrogen storage tanks it is possible to enhance the storage capability in terms of internal pressure and resistance to external loads and impacts. Most importantly the proposed concept would lead to a breakthrough in developing load-bearing energy storage devices. For the metamaterial core, hexagonal bending-dominated unit cell architecture with transversely curved connecting beam-like geometries would ensure the dual functionality of high specific stiffness and energy absorption capability which are mutually exclusive in traditional lattice metamaterials. The functionally graded beams, a periodic network of which constitutes the lattice, are modelled here using 3D degenerated shell elements in a finite element framework. Geometric nonlinearity using Green-Lagrange strain tensor is considered for an accurate analysis. The beam-level nonlinear deformation physics is integrated with the unit cell mechanics following a semi-analytical framework to obtain the effective in-plane and out-of-plane elastic moduli of the metamaterials. The numerical results show that the curved beam lattice metamaterials have significantly enhanced in-plane elastic properties than straight lattices along with a reduced disparity among the in-plane and out-of-plane elastic moduli.
... Hierarchical structures were used to modulate the characteristics by adjusting dimension ratios of different hierarchy [10]. A programmable deformation-dependent stiffness and shape modulation using distant actuation can be generated using an origami structure [11]. Recent literature also revealed the existence of negative Young's modulus and Poisson's ratio in some structures [12,13]. ...
... Origami-inspired metamaterials have been gaining significant attention for their unique ability to provide real-time programmable mechanical features particularly in the realm of shape morphing [1,2]. In this study, we proposed higher-order derivatives of Miura origami architecture such as inclined Arc Miura for achieving on-demand programmed pre-defined shape morphing under far-field actuation and state transition from twodimensional sheet to three-dimensional complex structure. ...
... Origami has sparked the emergence of a newly growing field of science and engineering that focuses on creating three-dimensional structures from two-dimensional pre-forms through a folding process [1,2]. In this study, we proposed a spatially graded derivative of Miura-based origami architecture such as graded Arc -Miura for achieving a wide range of programmable shape morphing capabilities. ...
... Recent advancements in the eld of mechanical metamaterials show that their design at the microscale can exhibit unprecedented novel physical properties like negative mass density, negative Poisson's ratio, ultra-lightweight characteristics, negative elastic moduli, crushing and specic energy absorption capacity, meta-uid characteristics, etc. [27,28,29,30,31,32,33,34,35,36,37,38,39]. Apart from meeting various unprecedented structural demands, the use of mechanical metamaterials can lead to optimized design with multi-functional abilities. ...
Analytical investigations to characterize the effective mechanical properties of lattice materials allow an in-depth exploration of the parameter space efficiently following an insightful, yet elegant framework. 2D lattice materials, which have been extensively dealt with in the literature following analytical as well as numerical and experimental approaches, have limitations concerning multi-directional stiffness and Poisson's ratio tunability. The primary objective of this paper is to develop mechanics-based formulations for a more complex analysis of 3D lattices, leading to a physically insightful analytical approach capable of accounting the beam-level mechanics of pre-existing intrinsic stresses along with their interaction with 3D unit cell architecture. We have investigated the in-plane and out-of-plane effective elastic properties to portray the physics behind the deformation of 3D lattices under externally applied far-field normal and shear stresses. The considered effect of beam-level intrinsic stresses therein can be regarded as a consequence of inevitable temperature variation, pre-stress during fabrication, inelastic and non-uniform deformation, manufacturing irregularities etc. Such effects can notably impact the effective elastic properties of lattice materials, quantifying which for 3D honeycombs is the central focus of this work. Further, from the material innovation viewpoint, the intrinsic stresses can be deliberately introduced to expand the microstructural design space for effective elastic property modulation of 3D lattices. This will lead to programming of effective properties as a function of intrinsic stresses without altering the microstructural geometry and lattice density. We have proposed a generic spectral framework of analyzing 3D lattices analytically, wherein the beam-level stiffness matrix including the effect of bending, axial, shear and twisting deformations along with intrinsic stresses can be coupled with the unit cell mechanics for obtaining the effective elastic properties.
... Metamaterials deal with global mechanical properties with periodic micro-structural design and intrinsic material distribution at the micro-scale, wherein the interplay between geometry and mechanics can bring about wonders in terms of eective physical properties [1]. Over the last decade, this eld of architected materials has received tremendous attention from the research community for the prospect of achieving unprecedented mechanical properties beyond the limits of conventional materials along with tunable multi-functional abilities such as extreme eective elastic moduli and stiness [2,3,4,5,6,7], negative Poisson's ratio [8,9,10,11,12], programmable constitutive behavior [13,14,15,16], high specic energy absorption capability [17,18,19,20,21], active modulation of mechanical properties [1,22,23,24], shape morphing [25,26,27,28,29,30], unusual acoustic parameters (for example, negative refractive index) [31], energy harvesting [32,33], vibration control [34,35,36] etc. ...
Bi-level tailoring of cellular metamaterials involving a dual design space of unit cell and elementary beam level architectures has recently gained traction for the ability to achieve extreme elastic constitutive properties along with modulating multi-functional mechanical behavior in an unprecedented way. This article proposes an efficient analytical approach for the accurate evaluation of all constitutive elastic constants of asymmetric multi-material variably-thickened hexagonal lattices by considering the combined effect of bending, stretching, and shearing deformations of cell walls along with their rigid rotation. A tri-member unit cell is conceptualized, wherein all nine constitutive constants are obtained through the mechanics under one cell wall direction and subsequent repetitive coordinate transformations. We enhance the design space of lattice metamaterials substantially here by introducing multiple exploitable dimensions such as asymmetric geometry, multi-material unit cells and variably-thickened cell walls, wherein the conventional monomaterial auxetic and non-auxetic hexagonal configurations can be analyzed as special cases along with other symmetric and asymmetric lattices such as a range of rectangular and rhombic geometries. The generic analytical approach along with extensive numerical results presented in this paper opens up new avenues for efficient optimized design of the next-generation multi-functional lattices and cellular metamaterials with highly tailored effective elastic properties.
... Such origami tubes need to be strictly designed to provide rigid foldability, due to complex mathematical models and motion mechanisms. Mukhopadhyay et al. [85] computationally and experimentally investigated the deformation mechanism and features of the waterbomb under compression. It was found that the waterbomb underwent a mixed mode Poisson's ratio, including rigid folding and structural deformation. ...
... Notably, the auxetic properties of origami-based structures have been observed in the Miura-ori [18][19][20][21] and water bomb tubes. [22][23][24] Re-entrant shapes within Tachi-Miura polyhedra (TMP) [25][26][27] also induce auxeticity. 27,28 Additionally, investigations into multidirectional auxeticity based on Miura-ori have been conducted. ...
Negative Poisson’s ratio in auxetic structures plays a crucial role in energy absorption and impact mitigation. Origami-based lattices within the realm of auxetic structures offer the advantage of facile fabrication and design. Nevertheless, the utilization of periodic lattices in origami-based auxetic structures constrains the available design space for achieving diverse mechanical properties. Addressing this limitation, our study introduces origami-based auxetic structures with functionally graded thickness, utilizing origami-based lattices known as Tachi–Miura polyhedra. We investigated the impact of functionally graded thickness on buckling behavior and force responses through dynamic loading experiments employing 3D-printed test pieces. The experimental results indicate that functionally graded thickness induces partial auxetic deformation in lattices, and the resulting nonsymmetric deformation prevents global buckling, thereby averting bounded forces observed in structures with uniform thickness. These findings extend the applicability of auxetic structures, spanning from energy absorption to the design of cushioning structures.
... Shape-adaptive mechanical metamaterials are a special class of mechanical materials, that employ motion, deformation or structural instabilities to change from one shape to a another desired form. Such metastructures have recently demonstrated potential for advanced functionalities, such as morphing in aircraft wings [1], adaptive flap of a wind turbine blade [2], topological wave guides [3], smart wearables [4] and biomedical devices [5]. The key to the tailored response of such metastructures lies in designing its constituent unit cells. ...
... We focused on an origami tessellation called waterbomb tube [27][28][29][30] and formulated the coupling folding motion of the modules as the recurrence relation, i.e., the discrete dynamical system, by solving the geometric constraints. We successfully identified the correspondence between quasiperiodic solutions of the derived dynamical system and nontrivial wavy folded states reported by Mukhopadhyay et al. 31 (see Figure 2). ...
Origami tessellations, origami whose crease pattern has translational symmetries, have attracted significant attention in designing the mechanical properties of objects. Previous origami-based engineering applications have been designed based on the “uniform-folding” of origami tessellations, where the folding of each unit cell is identical. Although “nonuniform-folding” allows for nonlinear phenomena that are impossible through uniform-folding, there is no universal model for nonuniform-folding, and the underlying mathematics for some observed phenomena remains unclear.
Wavy folded states that can be achieved through nonuniform-folding of the tubular origami tessellation called waterbomb tube are an example. Recently, the authors formulated the kinematic coupled motion of unit cells within waterbomb tube as the discrete dynamical system and identified a correspondence between its quasiperiodic solutions and wavy folded states. Here, we show that the wavy folded state is a universal phenomenon that can occur in the family of rotationally symmetric tubular origami tessellations. We represent their dynamical system as the composition of the two 2D mappings: taking the intersection of three spheres and crease pattern transformation. We show the universality of the wavy folded state through numerical calculation of phase diagrams and geometric proof of the system’s conservativeness. Additionally, we present a non-conservative tubular origami tessellation, whose crease pattern includes scaling. The result demonstrates the potential of the dynamical system model as a universal model for nonuniform-folding or a tool for designing metamaterials.
... Origami bellows [4] are created by folding planar origami patterns into closed hollow cylindrical structures; these include the Miura-ori [5], Kresling [6], and waterbomb [7] patterns. Such bellows are shown to have rich mechanical properties including multi-stability [5,8,9], self-locking behaviour [10,11], and tunable stiffness [12][13][14]. As such, origami bellows have been applied in fields such as robotics [15,16], meta-materials [17,18], binary switch [19], and B Mengzhu Yang mengzhu.yang@bristol.ac.uk 1 Department of Aerospace Engineering, University of Bristol, Bristol BS8 1TR, UK self-folding structures [20][21][22]. ...
Origami bellows are formed by folding flat sheets into closed cylindrical structures along predefined creases. As the bellows unfold, the volume of the origami structure will change significantly, offering potential for use as inflatable deployable structures. This paper presents a geometric study of the volume of multi-stable Miura-ori and Kresling bellows, focusing on their application as deployable space habitats. Such habitats would be compactly stowed during launch, before expanding once in orbit. The internal volume ratio between different deployed states is investigated across the geometric design space. As a case study, the SpaceX Falcon 9 payload fairing is chosen for the transportation of space habitats. The stowed volume and effective deployed volume of the origami space habitats are calculated to enable comparison with conventional habitat designs. Optimal designs for the deployment of Miura-ori and Kresling patterned tubular space habitats are obtained using particle swarm optimisation (PSO) techniques. Configurations with significant volume expansion can be found in both patterns, with the Miura-ori patterns achieving higher volume expansion due to their additional radial deployment. A multi-objective PSO (MOPSO) is adopted to identify trade-offs between volumetric deployment and radial expansion ratios for the Miura-ori pattern.
... The research projects described above are essentially based on static homogenization of the lattice systems. Indepth analysis in recent years has shown fascinating developments, such as ultralight metamaterials [15] approaching theoretical strength limit [16] negative refraction elastic waves [17], stiffness modulation [18,19], elastic cloaking [20,21], hyperbolic elastic metamaterials [22], composite panels [23], negative Poisson's ratio (auxetic) materials [24,25],bandgap exhibiting lattice structures [26], materials with negative effective elastic modulus [27], negative mass density [28], multi-physical and multi-material property modulation [29], meta-fluids [30] and nano-scale multi-functional properties [31]. These state-of-theart components are widely used in vibrating systems, such as wind turbines, aeronautical structures, and a wide range of electro-mechanical devices. ...
... Nowadays, origami is no longer limited to folding "paper", but refers to all practices that transform two-dimensional sheets with certain crease patterns into three-dimensional structures through folding. Folding shape and size changes, but also induces unique or extraordinary mechanical properties, which have attracted extensive research interest, and properties that have been uncovered including bi-stability and multi-stability [1,2], negative Poisson's ratio [3,4], negative and quasi-zero stiffness [5], programmable stiffness [6], programmable self-locking [7], recoverable collapse [8], etc. As a consequence, origamibased and origami-inspired structures and metamaterials have been applied in many fields, such as deployable space structures [9,10], self-deployable origami stent graft [11], origami robots [12,13], etc. ...
Multi-stable origami structures and metamaterials possess unique advantages and could exhibit multiple stable three-dimensional configurations, which have attracted widespread research interest and held promise for applications in many fields. Although a great deal of attention has been paid to the design and application of multi-stable origami structures, less knowledge is available about the transition sequence among different stable configurations, especially in terms of the fundamental mechanism and the tuning method. To fill this gap, with the multi-stable dual-cell stacked Miura-ori chain as a platform, this paper explores the rules that govern the configuration transition and proposes effective methods for tuning the transition sequence. Specifically, by correlating the energy evolution, the transition paths, and the associated force–displacement profiles, we find that the critical extension/compression forces of the component cells play a critical role in governing the transition sequence. Accordingly, we summarize the rules for predicting the transition sequence: the component cell that first reaches the critical force during quasi-static extension or compression will be the first to undergo a configuration switch. Based on these findings, two methods, i.e., a design method based on crease-stiffness assignment and an online method based on internal pressure regulation, are proposed to tune the stability profile and the transition sequence of the multi-stable origami structure. The crease-stiffness design approach, although effective, cannot be employed for online tuning once the prototype has been fabricated. The pressure-based approach, on the other hand, has been shown experimentally to be effective in adjusting the constitutive force–displacement profiles of the component cells and, in turn, tuning the transition sequence according to the summarized rules. The results of this study will advance the state of the art of origami mechanics and promote the engineering applications of multi-stable origami metamaterials.
... The mechanical characteristics of the origami tubes can be programmed by altering their geometric parameters [30][31][32]. Cai et al. [33] studied the geometric design and mechanical behavior of a deployable cylinder with Miura origami by using analytical and numerical methods. They confirmed that the geometric parameters had an impact on the dynamic mechanical behavior of the origami tube, but the pin-jointed framework adopted ignored the deformation of the origami panel. ...
... Articially engineered lattice-based materials, a class of mechanical metamaterials, exhibit mechanical properties which are not found in conventional structural materials directly obtained from nature [1]. Their microstructural design can result in unprecedented characteristics such as negative mass density, negative elastic moduli, auxeticity, ultra property characteristics like specic strength and stiness, lightweight features, meta-uid properties, tunable constitutive relations, active and programmable properties etc. [2,3,4,5,6,7,8,9,10]. They have attracted the scientic community due to their properties that span across dierent ranges catering to application-specic multi-functional demands of the modern industry. ...
Effective elastic moduli of lattice-based materials are one of the most crucial parameters for the adoption of such artificial microstructures in advanced mechanical and structural systems as per various application-specific demands. In conventional naturally occurring materials, these elastic moduli remain invariant under tensile and compressive normal modes or clock-wise and anti-clock-wise shear modes. Here we introduce programmed domain discontinuities in the cell walls of the unit-cells of lattice metamaterials involving a bi-level microstructural design to achieve non-invariant elastic moduli under tensile and compressive normal modes or clock-wise and anti-clock-wise shear modes. More interestingly, such non-invariance can be realized in the linear small deformation regime and the elastic moduli can be tailored to have higher or lower value in any mode compared to the other depending on the placement and intensity of the discontinuities in a programmable paradigm. We have derived an efficient analytical framework for the effective elastic moduli of lattice materials taking into account the influence of domain discontinuity. The axial and shear deformations at the beam level are considered along with bending deformation in the proposed analytical expressions. The numerical results ascertain that the domain discontinuities, in conjunction with unit cell level geometric parameters, can impact the effective elastic constants significantly under different modes of far-field stresses. It is further revealed that the degree of auxeticity of such lattices can be programmed to have target values (including non-invariance under different modes of deformation) as a function of the intensity and location of domain discontinuity when axial and shear deformations are included at the beam level. Realization of the unusual non-invariant elastic moduli of bi-level architected lattice materials would lead to a range of technologically demanding niche applications where one mode of deformation requires more or less force to deform compared to the opposite mode. Besides being able to perform as a load-bearing component, the proposed metamaterial can be used as an integrated sensor for measuring the level of stress or strain in structures.
... To realise adaptive damping properties without these limitations, integrating the geometrical design of a component as design parameter has shown promise in the area of mechanical metamaterials (Berwind et al., 2018;Lincoln et al., 2019;Surjadi et al., 2019;Fischer et al., 2020). This class of materials is based on unit cells that form artificial composites with unusual properties Berwind et al., 2018;Mukhopadhyay et al., 2020). The unit cells are designed with tailored mechanical elements inside the material and concepts for potential applications such as high energy shock absorbers (Morris et al., 2019;Chen et al., 2020) or specific acoustic properties have been published (Yang et al., 2010;Bückmann et al., 2012;Manimala and Sun, 2014;Cummer et al., 2016;Frenzel et al., 2016;Zhang et al., 2021). ...
A theoretical and experimental framework for novel metamaterial with programmable damping properties is presented. This material system is able to switch between elastic-dominated and damping-dominated regimes with different overall stiffness under dynamic loading depending on the external stimulus. The unit cell combines an auxetic and a bellow-like layer separated by an interface through which the amount of media flow can be tuned depending on the lateral strain. A simplified analytical model is derived to analyse the programmable damping effect. The model is further extended with a fluid-dynamics approach to link the effective damping properties with geometrical parameters to aid with the practical design of the metamaterial. Afterward, experiments are conducted on a macroscopic level using laser-sintered unit cells to validate the functionality of the concept both with air and water as media within the unit cells. To conclude the work, initial results on microscopic-level unit cells fabricated by two-photon lithography are introduced to showcase the scalability of the concept. This work provides an experimentally validated theoretical framework for future investigations to design unit cells with programmable damping on different length scales for applications requiring tailored dynamic energy dissipation.
... Therefore, origami has been widely used in surgical robots [27,28], soft robots [29,30], microrobots [14,31], and mechanical metamaterial [32,33] in recent years. By changing the arrangement of CPs, scientists have designed many classical origami CPs, including Waterbomb [34][35][36], Kresling [37][38][39], Yoshimura [25,40], Miura [41,42], Flasher [43,44], and Square-twist [45,46]. Among them, Waterbomb has two different motion paths [47], so it has great attention. ...
The structure of a traditional rigid bronchoscope includes proximal, distal, and body, representing an important means to treat hypoxic diseases. However, the body structure is too simple, resulting in the utilization rate of oxygen being usually low. In this work, we reported a deformable rigid bronchoscope (named Oribron) by adding a Waterbomb origami structure to the body. The Waterbomb’s backbone is made of films, and the pneumatic actuators are placed inside it to achieve rapid deformation at low pressure. Experiments showed that Waterbomb has a unique deformation mechanism, which can transform from a small-diameter configuration (#1) to a large-diameter configuration (#2), showing excellent radial support capability. When Oribron entered or left the trachea, the Waterbomb remained in #1. When Oribron is working, the Waterbomb transforms from #1 to #2. Since #2 reduces the gap between the bronchoscope and the tracheal wall, it effectively slows down the rate of oxygen loss, thus promoting the absorption of oxygen by the patient. Therefore, we believe that this work will provide a new strategy for the integrated development of origami and medical devices.
... In such materials, the effective properties are characterized by their structural configuration and not by their intrinsic material properties alone. We can modulate the global mechanical properties of mechanical metamaterials by controlling their microstructural geometric parameters, which can be tuned to present unprecedented novel characteristics like negative elastic moduli, auxetic characteristics, extreme multi-physical properties, meta-fluid properties, high crushing resistance, shock absorption characteristics, negative mass density, etc [1][2][3][4][5][6][7][8][9][10][11][12]. Lattice-based materials are a class of metamaterials that have a typical feature of unit cell periodicity [13][14][15][16][17]. ...
Engineered honeycomb lattice materials with high specific strength and stiffness along with the advantage of programmable direction-dependent mechanical tailorability are being increasingly adopted for various advanced multifunctional applications. To use these artificial microstructures with unprecedented mechanical properties in the design of different application-specific structures, it is essential to investigate the effective elastic moduli and their dependence on the microstructural geometry and the physics of deformation at the elementary level. While it is possible to have a wide range of effective mechanical properties based on their designed microstructural geometry, most of the recent advancements in this field lead to passive mechanical properties, meaning it is not possible to actively modulate the lattice-level properties after they are manufactured. Thus the on-demand control of mechanical properties is lacking, which is crucial for a range of multi-functional applications in advanced structural systems. To address this issue, we propose a new class of lattice materials wherein the beam-level multi-physical deformation behavior can be exploited as a function of external stimuli like magnetic field by considering hard magnetic soft (HMS) beams. More interestingly, effective property modulation at the lattice level would be contactless without the necessity of having a complex network of electrical circuits embedded within the microstructure. We have developed a semi-analytical model for the nonlinear effective elastic properties of such programmable lattice materials under large deformation, wherein the mechanical properties can be modulated in an expanded design space of microstructural geometry and magnetic field. The numerical results show that the effective properties can be actively modulated as a function of the magnetic field covering a wide range (including programmable state transition with on-demand positive and negative values), leading to the behavior of soft polymer to stiff metals in a single lattice microstructure according to operational demands.
... The eective material properties of these articially engineered lattice metamaterials depend upon the geometric conguration of the constituent unit cells in addition to the intrinsic material properties. Thus the macroscale material properties of these metamaterials can be tailored for specic applications and new advanced materials can be created with novel functionalities [9,10,11,12,13,14,15,16,17]. Note that the eective properties of lattice metamaterials are dened at a higher length scale (macroscale), wherein these properties are derived primarily based on a much lower scale periodic microstructure (dened by unit cells). ...
Conventional bending-dominated lattices exhibit less specific stiffness compared to stretching-dominated lattices while showing high specific energy absorption capacity. This article aims to improve the specific stiffness of bending-dominated lattices by introducing elementary-level programmed curvature through a multi-level hierarchical framework. The influence of curvature in the elementary beams is investigated here on the effective in-plane and out-of-plane elastic properties of lattice materials. The beam-like cell walls with out-of-plane curvature are modeled based on 3D degenerated shell finite elements. Subsequently, the beam deflections are integrated with unit cell level mechanics in an efficient semi-analytical framework to obtain the lattice-level effective elastic moduli. The numerical results reveal that the effective in-plane elastic moduli of lattices with curved isotropic cell walls can be significantly improved without altering the lattice-level relative density, while the effective out-of-plane elastic properties reduce due to the introduction of curvature. To address this issue, we further propose laminated composite cell walls with out-of-plane curvature based on the 3D degenerated shell elements, which can lead to holistic improvements in the in-plane and out-of-plane effective elastic properties. The proposed curved composite lattice materials would enhance the specific stiffness of bending-dominated lattices to a significant extent, while maintaining their conventional multi-functional advantages.
... By folding along all creases according to the default mountain-valley assignment, 3D origami structures can be obtained, such as the ''magic ball'' with positive Gaussian curvature. The waterbomb tessellations have been studied and applied, such as biomedical stents [12], adaptive freeform surface [13], deformable wheel robots [14], worn robots [15], and actuated tubular meta-structures [16]. Symmetric folding [17] and twist folding [18] have also been uncovered. ...
As a classical origami pattern, the waterbomb tessellation consisting of a set of waterbomb bases shows the potential to morph into three-dimensional surfaces by folding flat sheet materials. Here, we present an inverse-design method to approximate three-dimensional target surfaces based on this origami. First, we utilize the waterbomb base, in which six creases meet at the center, to generate a partially folded base mesh according to the target surface. Constraints of developability and flat-foldability are then solved through a gradient-based optimization on such a base mesh. In addition, we utilize the seven-crease waterbomb base, considered as a flat-foldable derivative of the six-crease waterbomb base, for approximating curved target surfaces. Another constraint of planarity is identified and solved, since the seven-crease waterbomb base contains two quads. Furthermore, we show the possibility of approximation via a combination of six- and seven-crease waterbomb bases. In optimization, Cartesian and parametric coordinates of vertices are adopted as unknown variables. We demonstrate the flexibility and validity of our method by illustrating a variety of origami approximations admitting geometric constraints. Our work not only facilitates the design of waterbomb tessellations as an art form, but also opens up avenues for future work on both theoretical structure analyses and novel engineering applications.
... Intense research has been performed recently on multi-physical and multi-material property modulation [21,22,23,24,25], nano-scale multi-functional properties [26,27,28], far-eld actuation dependent local shape and stiness modulation [29,30,31,32] and auxetic meta-materials [33,34]. Tremendous progress in the 3D printing and other manufacturing technologies [35,36,37] over the last decade has boosted the physical realization of complex metamaterial designs and experimental investigation for such lattices. ...
Architected lattice materials, realized through artificial micro‐structuring, have drawn tremendous attention lately due to their enhanced mechanical performances in multifunctional applications. However, the research area on the design of artificial microstructures for the modulation of mechanical properties is increasingly becoming saturated due to extensive investigations considering different possibilities of lattice geometry and beam‐like network design. Thus, there exists a strong rationale for innovative design at a more elementary level. It can enhance and grow the microstructural space laterally for exploiting the potential of geometries and patterns in multiple length scales, and the mutual interactions thereof. A bi‐level design is proposed, where besides having the architected cellular networks at an upper scale, the constituting beam‐like members at a lower scale are further topology‐engineered for most optimum material utilization. The coupled interaction of beam‐level and lattice‐level architectures can enhance the specific elastic properties to an extreme extent (up to ≈25 and 20 times, depending on normal and shear modes, respectively), leading to ultra‐lightweight multifunctional materials for critical applications under static and dynamic environments.
... Nasser et al. defined the smooth surfaces approximating the folded state of Miura-ori and eggbox-pattern by homogenizing the polyhedral surface using differential geometry [9,10]. Tubular waterbomb tessellation called waterbomb tube has the non-trivial behavior that their folded states can approximate wave-like surface [2,8]. In our previous work [3], we clarified the mathematics behind the wave-like surface; the oscillating configuration is generated by the quasi-periodic solutions of the discrete dynamical system that comes from the geometric constraints. ...
Folded surfaces of origami tessellations sometimes exhibit non-trivial behaviors, which have attracted much attention. The oscillation of tubular waterbomb tessellation is one example. Recently, the authors reported that the kinematics of waterbomb tube depends on the discrete dynamical system that arises from the geometric constraints between modules and quasi-periodic solutions of the dynamical system generate oscillating configurations. Although the quasi-periodic behavior is the characteristic of conservative systems, whether the system is conservative has been unknown. In this paper, we decompose the dynamical system of waterbomb tube into three steps and represent the one-step using the two kinds of mappings between zigzag polygonal linkages. By changing parameters of the mappings and composite them, we generalize the dynamical system of waterbomb tube to that of various tubular origami tessellations and show their oscillating configurations. Furthermore, by analyzing the mapping, we give proof of the conservation of the dynamical system.
In this article, a novel soft origami module is proposed to detect multi-directional bending. The module is inspired by the deformability and adaptability of the piezoelectric sensor and origami structure. The detection of applied bending was conducted by the deflection of the piezoelectric sensor, which was intended by the origami folding on carefully designed creases. The electric responses to the mechanical deformation were calibrated and measured using the motion tracking of the module and voltage data acquisition from the sensor. The experimental results showed that large bending of 45% in 4 directions can be monitored by the sensor outputs. It was also predicted by theoretical modeling based on the origami kinematics and piezoelectric sensing mechanism. Furthermore, soft origami joystick and adaptive finger phalanx were demonstrated to show the applicability of the module in the field of robotics. This study provides the guideline into establishing functional soft origami modules and insight for robotic applications.
In recent decades, origami has transitioned from a traditional art form into a systematic field of scientific inquiry, characterized by attributes such as high foldability, lightweight frameworks, diverse deformation modes, and limited degrees of freedom. Despite the abundant literature on smart materials, actuation methods, design principles, and manufacturing techniques, comprehensive reviews focusing on the mechanical properties of origami-inspired structures remain rare. This review aims to fill this void by analyzing and summarizing the significant studies conducted on the mechanical properties of origami-inspired structures from 2013 to 2023. We begin with an overview that includes essential definitions of origami, classical origami patterns, and their associated tessellated or stacked structures. Following this, we delve into the principal dynamic modeling method for origami and conduct an in-depth analysis of the key mechanical properties of origami-inspired structures. These properties include tunable stiffness, bistability and multistability, meta-mechanical properties demonstrated by origami-based metamaterials, and bio-inspired mechanical characteristics. Finally, we conclude with a comprehensive summary that discusses the current challenges and future directions in the field of origami-inspired structures. Our review provides a thorough synthesis of both the mechanical properties and practical applications of origami-inspired structures, aiming to serve as a reference and stimulate further research.
Research into programmable materials has attracted extraordinary interest since the nineties, when the term “programmable” was introduced for the first time. In its widest definition, the term is used to denote materials that are designed to be highly dynamic, either in shape and/or physical/functional properties, on-demand and in a precise, sequential predetermined way. Such unique feature allows them to adapt to various needs and offers new opportunities in several application fields, enabling them to overcome the limitations of traditional materials. The present paper aims to introduce readers to the world of programmable materials, enhance their interest, knowledge, and skills in the field, and provide useful insights and new ideas on how to approach their development and implementation. Accordingly, this paper offers an overview and discussion of current state-of-the-art and recent progress up to future perspectives. First, the historical evolution and definition of these materials as well as the types of programmable properties achievable are presented. Then, the different programming strategies that could be used to tune material properties are covered, with an emphasis on the constituent materials, applied stimuli, and geometrical arrangements. Finally, real-world applications, ongoing challenges, and future directions for this exciting class of materials are discussed.
Stiffness regulation strategies endow soft machines with stronger functionality to cope with diverse application requirements, for example manipulating heavy items by improving structural stiffness. However, most programmable stiffness strategies usually struggle to preserve the inherent compliant interaction capabilities following an enhancement in structural stiffness. In this study, inspired by the musculocutaneous system, we propose a soft stimuli‐responsive material (SRM) by combining shape memory alloy into compliant materials. By characterizing the mechanical performance, the flexural modulus increases from 6.6 to 142.4 MPa under the action of active stimuli, crossing two orders of magnitude, while Young's modulus stays at 2.2 MPa during programming structural stiffness. This comparative result indicates that our SRMs can keep a lower contact stiffness for compliant interaction although structural stiffness increases. Then, we develop three diverse soft machines to show the application potential of this smart material, such as robotic grippers, wearable devices, and deployable mechanisms. By applying our materials, these machines possess stronger load‐bearing capabilities. Meanwhile, these demonstrations also illustrate the efficacy of this paradigm in regulating the structural stiffness of soft machines while maintaining their compliant interaction capabilities.
Metamaterials have been a hot topic over the past 2 decades, involving scientific research directions in materials, engineering, and physics. Among them, programmable mechanical metamaterials are an emerging class of metamaterials that offer intelligent programming and control of diverse mechanical properties, such as stiffness, damping, thermal expansion, and shape memory behavior. Meanwhile, it can be rationally designed to have specific geometric architectures and programming strategies in response to different types of external stimuli, such as temperature, electric and magnetic fields, and mechanical loads. These intelligent mechanical properties have a wide range of potential applications due to their uniqueness and controllability, including soft robotics, adaptive structures, and wearable devices. Thus, the programming strategies to achieve them are particularly critical. Combined with related programmable thinking concepts, this paper briefly reviews programming strategies for programmable mechanical metamaterials, including geometric, structural, and external driving force programming. Meanwhile, this paper presents the principles of programming strategies classified according to different programmable mechanical properties (e.g., programmable stiffness, deformation, multistability) and looks ahead to the challenges and opportunities for future research.
In this paper, a novel cable-driven soft origami multimodal actuator is proposed. The proposed actuator comprises multiple origamis based on the Yoshimura pattern. The origami-based actuator performs both linear and bending motion by exploiting the unique folding state of the origami structure using a simple motor-cable system. The impact force and position of the tip on the actuator are experimentally demonstrated and the results are compared with mathematical models using folding mechanics. In the multi-modal origami structure, the actuator obtains high impact force, large bending angle, and large workspace with small size. To validate its performance, a pinch gripper with wide grasping range is also developed using a combination of the actuators.
We discuss the dynamics of a relatively simple origami-inspired structure considering discrete and continuum models. The latter was derived as a certain limit of the discrete model. Here we analyze small in-plane deformations and related equations of infinitesimal motions. For both models, dispersion relations were derived and compared. The comparison of the dispersion relations showed that the continuum model can capture the behavior of origami structures, which can be helpful in the materials properties determination and nondestructive evaluation.
This paper proposes a novel swimming robot with waterbomb origami wheel. The wheel of the swimming robot is a waterbomb origami that acts like a paddle blade. The origami wheel provides a new propulsion way for the swimming vehicle. The propulsion principle is to use the water flow to push the origami structure like the blade to propel it move forward. The analytical model describing the mechanical behavior of the origami wheel was built to illustrate the superior swimming characteristics of the robot. The model uncovers propulsive force variation with respect to origami structure parameters. The prototypes of the swimming robot are manufactured to analyze the influence of the structural parameters on their performances such as swimming speed, steering, and propulsive force. The analysis results showed that the proposed swimming robot has advantages such as high propulsion force and fast response. Meanwhile, it provides a guideline for the structural design of the origami wheel that enables it to be suitable to swim in the water. In a word, the origami wheel provides a light and efficient propulsion for swimming vehicles. The origami wheel provides a novel and simple propulsion way for swimming vehicles, and the structure promotes the development of a new class of swimming vehicles.
For the protection of the human head by energy absorption structures, a soft mechanical response upon contact with the head is required to mitigate the effect of impact, while a hard mechanical response for highly efficient energy absorption is required to stop the movement of the head. This study realized the opposite mechanical properties during head protection by transitioning the deformation mode from bending to auxetic compression. First, non-linear finite element (FE) models were constructed to numerically reproduce the bending behavior. The calculated force responses agreed well with forces in bending tests. Using the FE models, the EA structures with proper transition of deformation modes were designed and installed in the seat headrests of real vehicles. Head protection was evaluated by dynamic loading in sled testing, in which the force on the head of the crash test dummy was measured. The head injury criterion improved from 274 to 155, indicating the superior performance of the tested structures compared to that achieved by energy absorption structures based on steel plates. Moreover, the deformation of auxetic structures prevented neck bending by holding the head. These findings present new possibilities for effectively protecting the human body by mitigating impact, facilitating energy absorption, and ensuring head stability.
As an art of paper folding, origami has been widely explored by artists for centuries. Only in recent decades has it gained attention from mathematicians and engineers for its complex geometry and rich mechanical properties. The surge of origami-inspired metamaterials has opened a new window for designing materials and structures. Typically, to build origami structures, a sheet of material is folded according to the creaselines that are marked with compliant mechanisms. However, despite their importance in origami fabrication, such compliant mechanisms have been relatively unexplored in the setting of origami metamaterials. In this study, we explore the relationship between the design parameters of compliant mechanisms and origami mechanical properties. In particular, we employ single hinge crease and Kresling origami, representative examples of rigid and non-rigid origami units, fabricated using a double-stitch perforation compliant mechanism design. We conduct axial compression tests using different crease parameters and fit the result into the bar-hinge origami model consisting of axial and torsional springs. We extract the relationship between the spring coefficients and crease parameters using Gaussian process regression. Our result shows that the change in the crease parameter contributes significantly to each spring element in a very different manner, which suggests the fine tunability of the compliant mechanisms depending on the mode of deformation. In particular, the spring stiffness varies with the crease parameter differently for rigid and non-rigid origami, even when the same crease parameter is tuned. Furthermore, we report that the qualitative static response of the Kresling origami can be tuned between monostable and bistable, or linear and nonlinear, by only changing the crease parameter while keeping the same fold pattern geometry. We believe that our compiled result proffers a library and guidelines for choosing compliant mechanisms for the creases of origami mechanical metamaterials.
The unique merits of origami structures and origami metamaterials are the folding-induced shape reconfigurability and the associated evolution of mechanical properties. However, currently, there is a lack of mature solutions on how to achieve active tuning, and the tunability is stuck in static properties. Therefore, this study proposes a pneumatic scheme to overcome the above two bottleneck problems. Specifically, by integrating a pneumatic bladder with a monostable Yoshimura-ori structure, a pneumatic Yoshimura origami (PYO) cell is designed. Compared with the conventional approach making use of the origami multistability, the pressure scheme is simpler in design, more accurate in regulation, and richer in configurations. To exploit the PYO structure for tunable dynamics, the dynamic model is developed via a nonlinear system identification approach, in which the overall system, including the structure itself and the friction contact, is represented as a nonlinear spring-damper element, with the constitutive profile identified via the weighted least square method from the dynamic experimental data. Based on the developed model, the pressure tunability is then explored in a 6-cell PYO structure and a PYO metamaterial. Through comprehensive linear dispersion analyses and numerical simulations, we reveal that pressure could effectively tune the passbands of the 6-cell structure so that the transmission of vibration, at certain frequencies, can be qualitatively switched between amplification and attenuation; from another perspective, pressure could also be tailored for programming the stopbands of the PYO metamaterial to achieve the shift between propagation and prohibition. The results of this investigation could provide useful guidelines for the development of intelligent origami structures/metamaterials with excellent tunability, and meanwhile, open a new perspective of origami dynamics research.
Origami patterns can be used to inspire the designs of structural materials with beneficial properties, such as low strength-to-weight ratios. This study explores the design, manufacturing, and mechanical properties of three different origami-inspired shapes, as well as three different material combinations for each shape, through dynamic impact testing and quasi-static compression testing. The commonly studied Miura origami pattern will be compared to two uncommon patterns: a square-based pattern and a triangular-based pattern. The samples are 3D printed and the material combinations include one rigid and one flexible polylactic acid (PLA) sample, and one multi-material configuration with flexible PLA crease areas and rigid PLA origami faces. The rigid square sample was the most effective at absorbing a single drop-weight impact load and the flexible Miura pattern was most effective at absorbing impact loads when multiple drops were performed on the same sample. The rigid triangular structure withstood the highest loads during the quasi-static compression testing. A finite element model of the quasi-static compression test was built to enhance the analysis of the various tested configurations.
This chapter tries to move away from any magical context by examining, as scientifically as possible, how by various stimulations a form can change spatially or in functionality, alone in a homogeneous way or by association with materials. It summarizes the developments in 4D printing, with a focus on the materials and methods used for the manufacture of 4D printed objects and structures. Although printed structures exhibit self‐healing, self‐diagnosing, self‐acting and self‐sensing capabilities, etc., the chapter illustrates attractive possibilities and also highlights some difficulties. To meet the specificities of 4D printing, the actuators, integrated or not, must satisfy the following: a resolution below a certain threshold, allowing a given stroke, depending on the application, a reasonable speed and a mechanical strength adapted to the objective, and the ability to be totally or partially integrable in the 4D device.
Geometrical frustration induced anisotropy and inhomogeneity are explored to achieve unique properties of metamaterials that set them apart from conventional materials. According to Neumann's principle, to achieve anisotropic responses, the material unit cell should possess less symmetry. Based on such guidelines, we present a triclinic metamaterial system of minimal symmetry, which is originated from a Trimorph origami pattern with a simple and insightful geometry: a basic unit cell with four tilted panels and four corresponding creases. The intrinsic geometry of the Trimorph origami, with its changing tilting angles, dictates a folding motion that varies the primitive vectors of the unit cell, couples the shear and normal strains of its extrinsic bulk, and leads to an unusual Poisson's effect. Such effect, associated to reversible auxeticity in the changing triclinic frame, is observed experimentally, and predicted theoretically by elegant math formulae. The nonlinearities of the folding motions allow the unit cell to display three robust stable states, connected through snapping instabilities. When the tristable unit cells are tessellated, phenomena that resembles linear and point defects emerge as a result of geometric frustration. The frustration is reprogrammable into distinct stable and inhomogeneous states by arbitrarily selecting the location of a single or multiple point defects. The Trimorph origami demonstrates the possibility of creating origami metamaterials with symmetries that were hitherto non‐existent, leading to triclinic metamaterials with tunable anisotropy for potential applications such as wave propagation control and compliant micro‐robots. This article is protected by copyright. All rights reserved
Origami-inspired folding methods present novel pathways to fabricate three-dimensional (3D) structures from 2D sheets. A key advantage of this approach is that planar printing and patterning processes could be used prior to folding, affording enhanced surface functionality to the folded structures. This is particularly useful for 3D lattices, possessing very large internal surface areas. While folding polyhedral strut-based lattices has already been demonstrated, more complex, curved sheet-based lattices have not yet been folded due to inherent developability constraints of conventional origami. Here, a novel folding strategy is presented to fold flat sheets into topologically complex cellular materials based on triply periodic minimal surfaces (TPMS), which are attractive geometries for many applications. The approach differs from traditional origami by employing material stretching to accommodate non-developability. Our method leverages the inherent hyperbolic symmetries of TPMS to assemble complex 3D structures from a net of self-foldable patches. We also demonstrate that attaching 3D-printed foldable frames to pre-strained elastomer sheets enables self-folding and self-guided minimal surface shape adaption upon release of the pre-strain. This approach effectively bridges the Euclidean nature of origami with the hyperbolic nature of TPMS, offering novel avenues in the 2D-to-3D fabrication paradigm and the design of architected materials with enhanced functionality.
An insightful mechanics-based bottom-up framework is developed for probing the frequency-dependence of lattice material microstructures. Under a vibrating condition, effective elastic moduli of such microstructured materials can become negative for certain frequency values, leading to an unusual mechanical behaviour with a multitude of potential applications. We have derived the fundamental theoretical limits for the minimum frequency, beyond which the negative effective moduli of the materials could be obtained. An efficient dynamic stiffness matrix based approach is developed to obtain the closed-form limits, which can exactly capture the sub-wavelength scale dynamics. The limits turn out to be a fundamental property of the lattice materials and depend on certain material and geometric parameters of the lattice in a unique manner. An explicit characterization of the theoretical limits of negative elastic moduli along with adequate physical insights would accelerate the process of its potential exploitation in various engineered materials and structural systems under dynamic regime across the length-scales.
An insightful mechanics-based concept is developed for probing the frequency-dependence in in-plane elastic moduli of microstructured lattice materials. Closed-form expressions for the complex elastic moduli are derived as a function of frequency by employing the dynamic stiffness matrix of beam elements, which can exactly capture the sub-wavelength scale dynamics. It is observed that the two Poisson's ratios are not dependent on the frequency of vibration, while the amplitude of two Young's moduli and shear modulus increase significantly with the increase of frequency. The variation of frequency-dependent phase of the complex elastic moduli is studied in terms of damping factors of the intrinsic material. The tunable frequency-dependent behaviour of elastic moduli in lattice materials could be exploited in the pseudo-static design of advanced engineering structures which are often operated in a vibrating environment. The generic concepts presented in this paper introduce new exploitable dimensions in the research of engineered materials for potential applications in various vibrating devices and structures across different length-scales.
Developing mechanical metamaterials with programmable properties is an emerging topic receiving wide attention. While the programmability mainly originates from structural multistability in previously designed metamaterials, here it is shown that nonflat-foldable origami provides a new platform to achieve programmability via its intrinsic self-locking and reconfiguration capabilities. Working with the single-collinear degree-4 vertex origami tessellation, it is found that each unit cell can self-lock at a nonflat configuration and, therefore, possesses wide design space to program its foldability and relative density. Experiments and numerical analyses are combined to demonstrate that by switching the deformation modes of the constituent cell from prelocking folding to postlocking pressing, its stiffness experiences a sudden jump, implying a limiting-stopper effect. Such a stiffness jump is generalized to a multisegment piecewise stiffness profile in a multilayer model. Furthermore, it is revealed that via strategically switching the constituent cells' deformation modes through passive or active means, the n-layer metamaterial's stiffness is controllable among 2ⁿ target stiffness values. Additionally, the piecewise stiffness can also trigger bistable responses dynamically under harmonic excitations, highlighting the metamaterial's rich dynamic performance. These unique characteristics of self-locking origami present new paths for creating programmable mechanical metamaterials with in situ controllable mechanical properties.
Mechanical metamaterials are a sub-category of designer materials where the geometry of the material at the small-scale is rationally designed to give rise to unusual properties and functionalities. Here, we propose the concept of “action-at-a-distance” metamaterials where a specific pattern of local deformation is programmed into the fabric of (cellular) materials. The desired pattern of local actuation could then be achieved simply through the application of one single global and far-field force. We proposed graded designs of auxetic and conventional unit cells with changing Poisson’s ratios as a way of making “action-at-a-distance” metamaterials. We explored five types of graded designs including linear, two types of radial gradients, checkered, and striped. Specimens were fabricated with indirect additive manufacturing and tested under compression, tension, and shear. Full-field strain maps measured with digital image correlation confirmed different patterns of local actuation under similar far-field strains. These materials have potential applications in soft (wearable) robotics and exosuits.
Significance
Origami has been employed to build deployable mechanical metamaterials through folding and unfolding along the crease lines. These deployable structures are flexible in their deployment direction so that they can be easily collapsed along the same path they are deployed. Here we create an origami-inspired mechanical metamaterial with on-demand deployability and selective collapsibility: autonomous deployability from the collapsed state and selective collapsibility along two different paths, with low stiffness for one path and substantially high stiffness for another path. The created mechanical metamaterial yields load-bearing capability in the deployed direction while still possessing great deployability and collapsibility. The principle in this work can be utilized to design and create versatile origami-inspired mechanical metamaterials that can find many applications.
Generalized high-fidelity closed-form formulae are developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insightful analytical approach. Hexagonal nano-structural forms (top view) are common for nanomaterials with monoplanar (such as graphene, hBN) and multiplanar (such as stanene, MoS2) configurations. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. Shear modulus assumes an important role in characterizing the applicability of different two-dimensional nanomaterials and heterostructures in various nanoelectromechanical systems such as determining the resonance frequency of the vibration modes involving torsion, wrinkling and rippling behavior of two-dimensional materials. We have developed mechanics-based closed-form formulae for the shear modulus of monolayer nanostructures and multi-layer nano-heterostructures. New results of shear modulus are presented for different classes of nanostructures (graphene, hBN, stanene and MoS2) and nano-heterostructures (graphene-hBN, graphene-MoS2, graphene-stanene and stanene-MoS2), which are categorized on the basis of the fundamental structural configurations. The numerical values of shear modulus are compared with the results from scientific literature (as available) and separate molecular dynamics simulations, wherein a good agreement is noticed. The proposed analytical expressions will enable the scientific community to efficiently evaluate shear modulus of wide range of nanostructures and nanoheterostructures.
Two-dimensional and quasi-two-dimensional materials are important nanostructures because of their exciting electronic, optical, thermal, chemical and mechanical properties. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. For example, transition metal dichalcogenides such as MoS2 show promising electronic and piezoelectric properties, but their low mechanical strength is a constraint for practical applications. This barrier can be mitigated by considering graphene-MoS2 heterostructure, as graphene possesses strong mechanical properties. We have developed efficient closed-form expressions for the equivalent elastic properties of such multi-layer hexagonal nano-hetrostructures. Based on these physics-based analytical formulae, mechanical properties are investigated for different heterostructures such as graphene-MoS2, graphene-hBN, graphene-stanene and stanene-MoS2. The proposed formulae will enable efficient characterization of mechanical properties in developing a wide range of application-specific nano-heterostructures.
Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on 'bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.
An analytical framework is developed for investigating the effect of viscoelasticity on irregular hexagonal lattices. At room temperature many polymers are found to be near their glass temperature. Elastic moduli of honeycombs made of such materials are not constant, but changes in the time or frequency domain. Thus consideration of viscoelastic properties are essential for such honeycombs. Irregularity in lattice structures being inevitable from practical point of view, analysis of the compound effect considering both irregularity and viscoelasticty is crucial for such structural forms. On the basis of a mechanics based bottom-up approach, computationally efficient closed-form formulae are derived in frequency domain. The spatially correlated structural and material attributes are obtained based on Karhunen-Loève expansion, which is integrated with the developed analytical approach to quantify the viscoelastic effect for irregular lattices. Consideration of such spatially correlated behaviour can simulate the practical stochastic system more closely. The two effective complex Young’s moduli and shear modulus are found to be dependent on the viscoelastic parameters, while the two in-plane effective Poisson’s ratios are found to be independent of viscoelastic parameters and frequency. Results are presented in both deterministic and stochastic regime, wherein it is observed that the amplitude of Young’s moduli and shear modulus are significantly amplified in the frequency domain. The response bounds are quantified considering two different forms of irregularity, randomly inhomogeneous irregularity and randomly homogeneous irregularity. The computationally efficient analytical approach presented in this study can be quite attractive for practical purposes to analyse and design lattices with predominantly viscoelastic behaviour along with consideration of structural and material irregularity.
Lightweight materials that are simultaneously strong and stiff are desirable for a range of applications from transportation to energy storage to defense. Micro- and nanolattices represent some of the lightest fabricated materials to date, but studies of their mechanical properties have produced inconsistent results that are not well captured by existing lattice models. We performed systematic nanomechanical experiments on four distinct geometries of solid polymer and hollow ceramic (Al_2O_3) nanolattices. All samples tested had a nearly identical scaling of strength (σ_y) and Young's modulus (E) with relative density (ρ), ranging from σ_y ∝ ρ^(1.45) to ρ^(1.92) and E ∝ ρ^(1.41) to ρ^(1.83), revealing that changing topology alone does not necessarily have a significant impact on nanolattice mechanical properties. Finite element analysis was performed on solid and hollow lattices with structural parameters beyond those realized experimentally, enabling the identification of transition regimes where solid-beam lattices diverge from existing analytical theories and revealing the complex parameter space of hollow-beam lattices. We propose a simplified analytical model for solid-beam lattices that provides insight into the mechanisms behind their observed stiffness, and we investigate different hollow-beam lattice parameters that give rise to their aberrant properties. These experimental, computational and theoretical results uncover how architecture can be used to access unique lattice mechanical property spaces while demonstrating the practical limits of existing beam-based models in characterizing their behavior.
An analytical framework is developed for predicting the effective in-plane elastic moduli (longitudinal and transverse Young's modulus, Poisson's ratios and shear modulus) of irregular hexagonal lattices with generalized form of spatially random structural geometry. On the basis of a mechanics based bottom-up multi-step approach, computationally efficient closed-form formulae are derived in this article. As a special case when there is no irregularity, the derived analytical expressions reduce to the respective well known formulae of regular honeycombs available in literature. Previous analytical investigations include the derivation of effective in-plane elastic moduli for hexagonal lattices with spatially random variation of cell angles, which is a special case of the generalized form of irregularity in material and structural attributes considered in this paper. The present study also includes development of a highly generalized finite element code for obtaining equivalent elastic properties of random lattices, which is employed to validate the proposed analytical formulae. The statistical results of elastic moduli obtained using the developed analytical expressions and using direct finite element simulations are noticed to be in good agreement affirming the accuracy and validity of the proposed analytical framework. All the in-plane elastic moduli are found to be significantly influenced by spatially random irregularity resulting in a decrease of the mean values for the two Young's moduli and two Poisson's ratios, while an increase of the mean value for the shear modulus.
Origami has recently received significant interest from the scientific community as a building block for constructing metamaterials. However, the primary focus has been placed on their kinematic applications, such as deployable space structures and sandwich core materials, by leveraging the compactness and auxeticity of planar origami platforms. Here, we present volumetric origami cells -- specifically triangulated cylindrical origami (TCO) -- with tunable stability and stiffness, and demonstrate their feasibility as non-volatile mechanical memory storage devices. We show that a pair of origami cells can develop a double-well potential to store bit information without the need of residual forces. What makes this origami-based approach more appealing is the realization of two-bit mechanical memory, in which two pairs of TCO cells are interconnected and one pair acts as a control for the other pair. Using TCO-based truss structures, we present an experimental demonstration of purely mechanical one- and two-bit memory storage mechanisms.
The effect of stochasticity in mechanical behaviour of metamaterials is quantified in a probabilistic framework. The stochasticity has been accounted in the form of random material distribution and structural irregularity, which are often encountered due to manufacturing and operational uncertainties. An analytical framework has been developed for analysing the effective stochastic in-plane elastic properties of irregular hexagonal structural forms with spatially random variations of cell angles and intrinsic material properties. Probabilistic distributions of the in-plane elastic moduli have been presented considering both randomly homogeneous and randomly inhomogeneous stochasticity in the system, followed by an insightful comparative discussion. The ergodic behaviour in spatially irregular lattices is investigated as a part of this study. It is found that the effect of random micro-structural variability in structural and material distribution has considerable influence on mechanical behaviour of metamaterials.
An analytical framework has been proposed to analyze the effect of random structural irregularity in honeycomb core for natural frequencies of sandwich panels. Closed-form formulas have been developed for the out-of-plane shear moduli of spatially irregular honeycombs following minimum potential energy theorem and minimum complementary energy theorem. Subsequently an analytical approach has been presented for free-vibration analysis of honeycomb core sandwich panels to quantify the effect of such irregularity following a probabilistic paradigm. Representative results have been furnished for natural frequencies corresponding to low vibration modes of a sandwich panel with high length-to-width ratio. The results suggest that spatially random irregularities in honeycomb core have considerable effect on the natural frequencies of sandwich panels.
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
An analytical formulation has been developed in this article for predicting the equivalent elastic properties of irregular honeycombs with spatially random variations in cell angles. Employing unit-cell based approaches, closed-form expressions of equivalent elastic properties of regular honeycombs are available. Closed-form expressions for equivalent elastic properties of irregular honeycombs are very scarce in available literature. In general, direct numerical simulation based methods are prevalent for this case. This paper proposes a novel analytical framework for predicting equivalent in-plane elastic moduli of irregular honeycombs using a representative unit cell element (RUCE) approach. Using this approach, closed-form expressions of equivalent in-plane elastic moduli (longitudinal and transverse Young’s modulus, shear modulus, Poisson’s ratios) have been derived. The expressions of longitudinal Young’s modulus, transverse Young’s modulus, and shear modulus are functions of both structural geometry and material properties of irregular honeycombs, while the Poisson’s ratios depend only on structural geometry of irregular honeycombs. The elastic moduli obtained for different degree of randomness following the proposed analytical approach are found to have close proximity to direct finite element simulation results.
Truss-based lattice materials are cellular materials with an outstanding potential for multi-functional use. This is owing to properties of high compressive strength to density ratios combined with a periodic and open structure. However, such structures at low relative densities are particularly vulnerable to elastic buckling failure. Fibre-reinforcement that increases the buckling strength of lattice materials is proposed and the behaviour of unit cells that are tessellated within the lattice is investigated. A two-dimensional square orientated unit cell and a three-dimensional tetrahedron-shaped unit cell are both modelled discretely using energy principles with the nonlinear interactive buckling behaviour being analysed. The analytical approach, based on a perturbation method, exhibits excellent agreement for the mechanical response when compared to results from numerical continuation for moderately large displacements. A fundamental understanding of the mechanical behaviour of a unit cell can be upscaled in future work. It is postulated that this will enable the determination of the constitutive behaviour of such lattice materials.
We explore the surprisingly rich energy landscape of origami-like folding
planar structures. We show that the configuration space of rigid-paneled
degree-4 vertices, the simplest building blocks of such systems, consists of at
least two distinct branches meeting at the flat state. This suggests that
generic vertices are at least bistable, but we find that the nonlinear nature
of these branches allows for vertices with as many as five distinct stable
states. In vertices with collinear folds and/or symmetry, more branches emerge
leading to up to six stable states. Finally, we introduce a procedure to tile
arbitrary 4-vertices while preserving their stable states, thus allowing the
design and creation of multistable origami metasheets.
Although broadly admired for its aesthetic qualities, the art of origami is now being recognized also as a framework for mechanical
metamaterial design. Working with the Miura-ori tessellation, we find that each unit cell of this crease pattern is mechanically
bistable, and by switching between states, the compressive modulus of the overall structure can be rationally and reversibly
tuned. By virtue of their interactions, these mechanically stable lattice defects also lead to emergent crystallographic structures
such as vacancies, dislocations, and grain boundaries. Each of these structures comes from an arrangement of reversible folds,
highlighting a connection between mechanical metamaterials and programmable matter. Given origami’s scale-free geometric character,
this framework for metamaterial design can be directly transferred to milli-, micro-, and nanometer-size systems.
T cells that accompany allogeneic hematopoietic grafts for treating leukemia enhance engraftment and mediate the graft-versus-leukemia
effect. Unfortunately, alloreactive T cells also cause graft-versus-host disease (GVHD). T cell depletion prevents GVHD but
increases the risk of graft rejection and leukemic relapse. In human transplants, we show that donor-versus-recipient natural
killer (NK)–cell alloreactivity could eliminate leukemia relapse and graft rejection and protect patients against GVHD. In
mice, the pretransplant infusion of alloreactive NK cells obviated the need for high-intensity conditioning and reduced GVHD.
NK cell alloreactivity may thus provide a powerful tool for enhancing the efficacy and safety of allogeneic hematopoietic
transplantation.
The tubular acoustic metamaterial with the double negativity based on the membranes and side holes periodically distributed along a pipe is studied with the Bloch theory. The results are verified by the full-wave simulation method and are used to explain the related experimental phenomena: the low-frequency forbidden band starting from the zero Hertz and the relations between the cutoff frequencies of the forbidden and pass bands in the single negativity metamaterials and the double negativity metamaterial composed of them. Based on the Bloch theory, the structural parameters of the membranes and side holes in the metamaterial are optimized to achieve the maximum pass band with the negative phase velocity (PBNV) since the PBNV is determined by the coactions of the membranes and side holes. Furthermore, the structures of the metamaterials are improved in order to broaden the PBNV further and achieve the balanced condition simultaneously.
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.
Origami is the archetype of a structural material with unusual mechanical
properties that arise almost exclusively from the geometry of its constituent
folds and forms the basis for mechanical metamaterials with an extreme
deformation response. Here we consider a simple periodically folded structure
Miura-ori, which is composed of identical unit cells of mountain and valley
folds with four-coordinated ridges, de?fined completely by 2 angles and 2
lengths. We use the geometrical properties of a Miura-ori plate to characterize
its elastic response to planar and non-planar piece- wise isometric
deformations and calculate the two-dimensional stretching and bending response
of a Miura-ori sheet, and show that the in-plane and out-of-plane Poisson's
ratios are equal in magnitude, but opposite in sign. Our geometric approach
also allows us to solve the inverse design problem of determining the geometric
parameters that achieve the optimal geometric and mechanical response of such
structures.
We show that any continuous flex that preserves the edge lengths of a closed triangulated surface of any genus in three-space must flex in such a way that the volume it bounds stays constant during the flex. 1.
An analytical framework has been developed for predicting the equivalent in-plane elastic moduli (longitudinal and transverse Young’s modulus, shear modulus, Poisson’s ratios) of irregular auxetic honeycombs with spatially random variations in cell angles. Employing a bottom up multi-scale based approach, computationally efficient closed-form expressions have been derived in this article. This study also includes development of a highly generalized finite element code capable of accepting number of cells in two perpendicular directions, random structural geometry and material properties of irregular auxetic honeycomb and thereby obtaining five in-plane elastic moduli of the structure. The elastic moduli obtained for different degree of randomness following the analytical formulae have been compared with the results of direct finite element simulations and they are found to be in good agreement corroborating the validity and accuracy of the proposed approach. The transverse Young’s modulus, shear modulus and Poisson’s ratio for loading in transverse direction (effecting the auxetic property) have been found to be highly influenced by the structural irregularity in auxetic honeycombs.
The waterbomb pattern is a well-known origami pattern and has been employed to construct foldable cylinders as stent grafts and deformable robot wheels. It is known that the cylinders made from the waterbomb pattern are, in general, not rigidly foldable. This feature makes construction and numerical simulation of those cylinders difficult because a distortion-free initial configuration for the cylinders cannot be identified. A geometrical analysis of the cylinders formed from the waterbomb pattern reveals that by properly selecting pattern geometry, there exist particular configurations at which a cylinder of a uniform radius can be rigidly assembled out of the pattern. In other words, the pattern can be perfectly connected together to form a cylinder without distortion. Those particular configurations can be used as the initial configuration of the cylinders when they are constructed and as the starting configuration of the cylinders in a numerical analysis.
Copyright © 2014 by ASME Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature
Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal
Perforated systems with quasi-disordered arrays of slits are found to exhibit auxetic characteristics almost as much as their traditional ordered "rotating-squares" counterparts. This provides a highly robust methodology for constructing auxetics that may be used for various practical applications such as skin grafting, where a high degree of precision may not always be achievable.
Significance
Origami, the ancient art of folding paper, has recently emerged as a method for creating deployable and reconfigurable engineering systems. These systems tend to be flexible because the thin sheets bend and twist easily. We introduce a new method of assembling origami into coupled tubes that can increase the origami stiffness by two orders of magnitude. The new assemblages can deploy through a single flexible motion, but they are substantially stiffer for any other type of bending or twisting movement. This versatility can be used for deployable structures in robotics, aerospace, and architecture. On a smaller scale, assembling thin sheets into these tubular assemblages can create metamaterials that can be deployed, stiffened, and tuned.
Origami is used beyond purely aesthetic pursuits to design responsive and customizable mechanical metamaterials. However, a generalized physical understanding of origami remains elusive, owing to the challenge of determining whether local kinematic constraints are globally compatible and to an incomplete understanding of how the folded sheet's material properties contribute to the overall mechanical response. Here, we show that the traditional square twist, whose crease pattern has zero degrees of freedom (DOF) and therefore should not be foldable, can nevertheless be folded by accessing bending deformations that are not explicit in the crease pattern. These hidden bending DOF are separated from the crease DOF by an energy gap that gives rise to a geometrically driven critical bifurcation between mono- and bistability. Noting its potential utility for fabricating mechanical switches, we use a temperature-responsive polymer-gel version of the square twist to demonstrate hysteretic folding dynamics at the sub-millimetre scale.
In this paper, we present a deformable wheel robot using the ball-shaped waterbomb origami pattern, so-called magic-ball pattern. The magic-ball origami pattern is a well-known pattern that changes its shape from a long cylindrical tube to a flat circular tube. By using this special structure, a wheel with mechanical functionalities can be achieved without using many mechanical parts. Moreover, because of the characteristic that the structure constrains its own movement, it is possible to control the whole shape of the wheel using only few actuators. And also, from analysis of the wheel structure in kinematic model, the performance of the wheel and determine the condition for actuators can be predicted. We think that the proposed design for the deformable wheel shows the possibility of using origami structure as a functional structure with its own mechanism.
We consider the axial buckling of a thin-walled cylinder fitted onto a mandrel core with a prescribed annular gap. The buckling pattern develops fully and uniformly to yield a surface texture of regular diamond-shaped buckles, which we propose for novel morphing structures. We describe experiments that operate well into the postbuckling regime, where a classical analysis does not apply; we show that the size of buckles depends on the cylinder radius and the gap width, but not on its thickness, and we formulate simple relationships from kinematics alone for estimating the buckle proportions during loading.
This paper presents an origami-inspired technique which allows the application of 2-D fabrication methods to build 3-D robotic systems. The ability to design robots as origami structures introduces a fast and low-cost fabrication method to modern, real-world robotic applications. We employ laser-machined origami patterns to build a new class of robotic systems for mobility and manipulation. Origami robots use only a flat sheet as the base structure for building complicated bodies. An arbitrarily complex folding pattern can be used to yield an array of functionalities, in the form of actuated hinges or active spring elements. For actuation, we use compact NiTi coil actuators placed on the body to move parts of the structure on-demand. We demonstrate, as a proof-of-concept case study, the end-to-end fabrication and assembly of a simple mobile robot that can undergo worm-like peristaltic locomotion.
This paper describes the design, manufacturing and properties of a new type of stent graft, the origami stent graft. Unlike conventional stent grafts which consist of a wire mesh stent and a covering membrane, the new origami stent graft is made from a single foldable foil with hill and valley folds. The Ni-rich titanium/nickel (TiNi) shape memory alloy (SMA) foil made by the newly developed ultrafine laminates method was used in order to produce the stent graft. The pattern of folds on the foil was produced by negative photochemical etching. The deployment of the stent graft is achieved either by SMA effect at the body temperature or by making use of property of superelasticity. A number of prototypes of the stent graft, which are the same size as standard oesophageal and aortal stent grafts, have been produced successfully. It was demonstrated that the stent graft deploy as expected.
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