Morphing flat sheets into non-planar shapes enables fast and scalable manufacturing of three-dimensional objects. Here, we investigate the out-of-plane shape morphing capabilities of single-material elastic sheets with architected cut patterns. The sheets are laser-cut into an array of tiles connected by flexible hinges, which enable large deformations with small applied forces. We demonstrate that a non-periodic cut pattern can make a sheet buckle into selectable three-dimensional shapes, such as domes or patterns of wrinkles, when pulled at specific boundary points. These global buckling modes are observed in experiments, predicted by numerical simulations, and rationalized by a kinematic analysis that highlights the role of the geometric frustration arising from nonperiodicity. The study focuses initially on elastic sheets, and is later extended to sheets made of elastic-plastic materials, which can retain their shape upon load removal. arXiv:1806.10851v1 [cond-mat.soft]

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Energy absorbing materials, like foams used in protective equipment, are able to undergo large deformations under low stresses, reducing the incoming stress wave below an injury or damage threshold. They are typically effective in absorbing energy through plastic deformation or fragmentation. However, existing solutions are passive, only effective against specific threats and they are usually damaged after use. Here, we overcome these limitations designing energy absorbing materials that use architected lattices filled with granular particles. We use architected lattices to take advantage of controlled bending and buckling of members to enhance energy absorption. We actively control the negative pressure level within the lattices, to tune the jamming phase transition of the granular particles, inducing controllable energy absorption and recoverable deformations. Our system shows tunable stiffness and yield strength by over an order of magnitude, and reduces the transmitted impact stress at different levels by up to 40% compared to the passive lattice. The demonstrated adaptive energy absorbing system sees wide potential applications from personal protective equipment, vehicle safety systems to aerospace structures.Architected lattices are materials whose properties arise from the selection of both their constitutive materials and the geometry of their micro-and meso-structure [1-5]. Architected materials have been proposed as new energy absorbing solutions with recoverable deformation, for example, taking advantage of mechanical instabilities in their underlying structure [6][7][8]. Although reusable, these solutions are intrinsically passive, with properties fixed once fabricated, and effective in mitigating impact loads under predefined velocities or energies. Most practical applications, however, require adaptive structures whose mechanical properties can be tuned to absorb or dissipate varying amounts of energy, in response to different impact conditions. Solutions to tune the mechanical properties of materials and structures [9,10] include the use of hydrogels that respond to temperature, pH, light and water content [11,12]; shape memory alloys and polymers (SMAs and SMPs) [13,14]; liquid crystal elastomers (LCEs) that respond to temperature and light [15,16]; and magnetorheological (MR) and electroactive polymers (EAPs) [17][18][19]. However, these materials either are mechanically too soft for engineering applications (hydrogels), require large temperature changes (LCEs), need re-programming at high