Multi-step self-guided pathways for shape-changing metamaterials

Coulais, Corentin; Sabbadini, Alberico; Vink, Fré; Hecke, Martin van

doi:10.1038/s41586-018-0541-0

Cited by 185 publications

(134 citation statements)

References 32 publications

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“…Mechanisms are collections of rigid elements linked by flexible hinges, designed to allow for a collective, floppy motion of the elements. More recently, floppy modes and mechanisms have received renewed attention in the context of mechanical metamaterials, which are architected materials designed to exhibit anomalous mechanical properties, including negative response parameters, shape morphing, and self-folding [6,7,[12][13][14][15][16][17][18][19][20][21][22]]. An important design strategy for mechanical metamaterials borrows the geometric design of mechanisms, and replaces their hinges by flexible parts which connect stiffer elements [22].…”

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confidence: 99%

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Excess floppy modes and multibranched mechanisms in metamaterials with symmetries

Lubbers

Hecke

2019

Phys. Rev. E

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Floppy modes -deformations that cost zero energy -are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in e.g. mechanical metamaterials, can feature an unlimited number of excess floppy modes that are absent in generic geometries, and in addition can support floppy modes that are multi-branched. We study the number ∆ of excess floppy modes by comparing generic and symmetric geometries with identical topologies, and show that ∆ is extensive, peaks at intermediate connection densities, and exhibits mean field scaling. We then develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, we leverage our insights to design metamaterials with multiple folding mechanisms.Floppy modes (FMs) play a fundamental role in the mechanics of a wide variety of disordered physical systems, from elastic networks [1-7] to jammed particle packings [8][9][10]. Floppy modes also play a role in many engineering problems, ranging from robotics to deployable structures, where the goal is to design structures that feature one or more mechanisms [11]. Mechanisms are collections of rigid elements linked by flexible hinges, designed to allow for a collective, floppy motion of the elements. More recently, floppy modes and mechanisms have received renewed attention in the context of mechanical metamaterials, which are architected materials designed to exhibit anomalous mechanical properties, including negative response parameters, shape morphing, and self-folding [6,7,[12][13][14][15][16][17][18][19][20][21][22]]. An important design strategy for mechanical metamaterials borrows the geometric design of mechanisms, and replaces their hinges by flexible parts which connect stiffer elements [22]. In all these examples, understanding how the geometric design controls the number and character of the floppy modes plays a central role.For systems consisting of objects with a total of n d degrees of freedom, connected by hinges that provide n c constraints, the number of non-trivial floppy modes n f and states of self-stress n ss are related by Maxwell-Calladine counting as n f − n ss = n d − n c − n rb where n rb counts the trivial rigid body modes (n rb = 3 in two dimensions) [23]. For generic, disordered systems n f and n ss can be determined separately from the connection topology [1, 2], but when symmetries are present such approaches break down and counting only yields the difference n f − n ss . For example, spring lattices which feature perfectly aligned bonds can generate excess floppy modes (and associated states of self stress) that disappear under generic perturbations and thus escape topology-based counting methods [1,2,[24][25][26][27][28][29]. Mechanical metamaterials often feature symmetric architectures where excess (a) (b) θ × FIG. 1. (color online) (a) N × N systems of...

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“…Here we address two key issues. First, what is the multiplicity and statistics of EFMs in diluted lattices as considered recently [21,36,37] [Fig. 1(b)].…”

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confidence: 99%

Excess floppy modes and multibranched mechanisms in metamaterials with symmetries

Lubbers

Hecke

2019

Phys. Rev. E

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“…This arrangement facilitates complicated mechanical behavior under external stimuli, and the literature is full of articles devoted to analysis of the unconventional mechanics of MOFs. [170] Metamaterials also demonstrate unconventional mechanical behavior. ), which is characterized by the different interactions (mechanical, electromagnetic) between the central element, a meta atom of a specific shape and size, with its neighbors.…”

Section: Mechanical Metamaterialsmentioning

confidence: 99%

Metal–Organic Frameworks in Modern Physics: Highlights and Perspectives

et al. 2019

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Owing to the synergistic combination of a hybrid organic–inorganic nature and a chemically active porous structure, metal–organic frameworks have emerged as a new class of crystalline materials. The current trend in the chemical industry is to utilize such crystals as flexible hosting elements for applications as diverse as gas and energy storage, filtration, catalysis, and sensing. From the physical point of view, metal–organic frameworks are considered molecular crystals with hierarchical structures providing the structure‐related physical properties crucial for future applications of energy transfer, data processing and storage, high‐energy physics, and light manipulation. Here, the perspectives of metal–organic frameworks as a new family of functional materials in modern physics are discussed: from porous metals and superconductors, topological insulators, and classical and quantum memory elements, to optical superstructures, materials for particle physics, and even molecular scale mechanical metamaterials. Based on complementary properties of crystallinity, softness, organic–inorganic nature, and complex hierarchy, a description of how such artificial materials have extended their impact on applied physics to become the mainstream in material science is offered.

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“…Mechanical metamaterials are artificially designed structures that offer extreme and unusual, yet useful, mechanical properties determined by their structural and geometric configurations rather than only intrinsic material properties of their composing elements. Conventional mechanical metamaterials are often formed by quasi-1D rods or links [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Folding of Tubular Waterbomb

Feng

Chen

et al. 2020

Research

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Origami has recently emerged as a promising building block of mechanical metamaterials because it offers a purely geometric design approach independent of scale and constituent material. The folding mechanics of origami-inspired metamaterials, i.e., whether the deformation involves only rotation of crease lines (rigid origami) or both crease rotation and facet distortion (nonrigid origami), is critical for fine-tuning their mechanical properties yet very difficult to determine for origami patterns with complex behaviors. Here, we characterize the folding of tubular waterbomb using a combined kinematic and structural analysis. We for the first time uncover that a waterbomb tube can undergo a mixed mode involving both rigid origami motion and nonrigid structural deformation, and the transition between them can lead to a substantial change in the stiffness. Furthermore, we derive theoretically the range of geometric parameters for the transition to occur, which paves the road to program the mechanical properties of the waterbomb pattern. We expect that such analysis and design approach will be applicable to more general origami patterns to create innovative programmable metamaterials, serving for a wide range of applications including aerospace systems, soft robotics, morphing structures, and medical devices.

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Multi-step self-guided pathways for shape-changing metamaterials

Cited by 185 publications

References 32 publications

Excess floppy modes and multibranched mechanisms in metamaterials with symmetries

Excess floppy modes and multibranched mechanisms in metamaterials with symmetries

Metal–Organic Frameworks in Modern Physics: Highlights and Perspectives

Folding of Tubular Waterbomb

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