A programmable auxetic metamaterial with tunable crystal symmetry

Anisotropic Morphing in Bistable Kirigami through Symmetry Breaking and Geometric Frustration

“…To conclude, our combined semi‐analytical, experimental, and numerical investigations have shown that symmetry breaking of slit pattern induces geometric frustration and anisotropic shape morphing in bistable kirigami and controls the trade‐offs between bistability and anisotropy of scaling. While symmetry breaking has been used to generate anisotropic response in other metamaterial architectures, [ 29,41,44,52 ] this work unlocks anisotropic morphing in kirigami metamaterials and further unveils how symmetry groups affect geometric frustration and their anisotropic bistable shape shifting. For example, “p31m” BAM with threefold rotational symmetry features frustration‐free bistable isotropic expansion, “cm” ABAM with lower symmetry undergoes frustrated anisotropic deployment with reduced bistability, and “p1” ABAM with least symmetry exhibits a moderate response that is frustrated and bounded by “cm” ABAM.…”

“…[24][25][26][27] The diverse set of properties and functionality that a planar kirigami pattern can deliver stems mainly from the tessellation of its repeating shape, e.g., triangular (kagome pattern), square, hexagonal, and other polygonal tiles, each embedding an intrinsic symmetry of their constituent slits, e.g., rotational, reflectional, and glide reflectional symmetry. [28][29][30][31][32][33] While ordinary kirigami patterns have been extensively studied for both their linear and nonlinear responses, other less trivial motifs of threefold and fourfold rotational symmetry have attracted attention for being able to offer bistable auxetic deployment with reconfiguration into states of preserving shape. [3] Other studies have focused on more complex incision patterns, e.g., hierarchical [1,34] and fractal tilings, [35,36] with reduced order of symmetry as well as beyond periodicity, e.g., randomly oriented [4] and other aperiodic patterns, [37,38] all contributing to yield a plethora of kinematic and mechanical responses.…”

“…[41] Symmetry has long been a valuable tool for creating complex architected materials. [41][42][43][44] However, for kirigami metamaterials it has only been applied to rigid deployable patterns [28,29,45] with kinematics described by nondeformable panels and pure rotational hinges. The deployment of all these patterns does not involve geometric frustration, [46,47] a phenomenon occurring when incompatible geometric constraints impede the deformation of an object under a set of applied forces; in the realm of kirigami, geometric frustration appears as local disordered deployments caused by incompatible geometric restrictions, such as local deformation of panels due to slit geometry that violates rigid deployable constraints [48] and out-of-plane morphing due to nonuniform strains in nonperiodic patterns.…”

Mechanical metamaterials for sports helmets: structural mechanics, design optimisation, and performance

“…They can be fabricated from conventional materials such as foam [306,307] or textiles [51,308], or designed as periodical/graded cellular structures [12][13][14]309]. Mechanical metamaterials can also be made from sheets of material by folding (known as origami) [310][311][312][313][314][315][316][317][318][319][320][321][322][323][324][325][326][327], or by folding, cutting, and joining (known as kirigami) [17, [328][329][330][331][332][333][334][335][336][337][338][339][340][341][342][343][344]. With high levels of control over end properties-given the additional degrees of design freedom afforded by controlling topology and base material-mechanical metamaterials are well suited to addressing complex engineering problems, like impact protection [17,50,262].…”

“…With high levels of control over end properties-given the additional degrees of design freedom afforded by controlling topology and base material-mechanical metamaterials are well suited to addressing complex engineering problems, like impact protection [17,50,262]. The common forms of unusual mechanical properties are auxetic (negative Poisson's ratio) behaviour (covered extensively in various reviews [46,50,307,309,345,346] and textbooks [308,347,348]), negative stiffness [349][350][351][352][353][354][355][356], shape morphing [337,[357][358][359], force/torque coupling [360][361][362][363][364], active/adaptive behaviour [351,[365][366][367], or programmable properties that are tuned to a specific application [17,26,28,341,361].…”