Session X57: Mechanical Metamaterials II

Bidirectional Folding with Atomic Layer Deposition Bimorphs for Autonomous Micro-Origami

We present micron sized self-folding structures that consist of nanometer-thin, atomic layer deposited SiO₂-Si₃N₄bilayers, built with conventional semiconductor fabrication methods. A bending response originating from strain differentials within these bilayer stacks is used as the fold actuation mechanism. This strain differential induced bending is controlled by ion exchange reactions in our nanoscale sheets, enabling us to produce radii of curvature at the order of microns within fractions of a second. By lithographically patterning these sheets and localizing the bending using flat photoresist panels, we create microscale origami devices that can sense chemical changes in their environment and respond by changing configurations according to prescribed mountain-valley fold patterns. Finally, we show that our fabrication approach offers a range of chemical, electrical and biological functions as well as a path to sequential folding through the programming of stacks.
  

Computational design of multistable metamaterials

Metamaterials’ properties arise not only from their chemical composition, but mainly from their periodic structure. While most of these materials are characterized by a fixed geometry, some materials are designed with internal hinging mechanisms. This allows them to be reconfigured with external stimuli, therefore exhibiting tuneable properties. However, these materials become dependent on the stimuli, and once removed the material will relax to the initial configuration. Previously we proposed a design strategy based on space-filling extruded polyhedra to create 3D reconfigurable materials comprising a periodic assembly of rigid plates and elastic hinges. Interestingly, for some of these structures we found additional stable configurations that are spatially admissible, but that cannot be reached without temporarily deforming the rigid faces. Here, we soften this constraint to open up new folding pathways. We introduce a computational approach to scan the energy landscape of these complex 3D structures, and show that our method closely mimics experimental implementations of locally actuated metamaterials. Using this approach, we find a wealth of multistable unit cells that can be assembled to create responsive materials capable of switching between different properties.   

Programmable Anisotropic Multi-stability in an Origami-inspired Metamaterial

In this project, we design, develop, fabricate and study a new class of 3D origami-inspired metamaterials with highly anisotropic mechanical instability and controlled reconfigurability. This metamaterial is constructed by connecting star-shaped units that are formed by folding an array of interconnected Miura-ori patterns, also known as origami string. The origami string is a one degree of freedom slender mechanisms in which we substituted paper and creases with 3D printed faces and revolute hinges, respectively. The star-shaped unit exhibits mechanically rich and strongly nonlinear behavior that includes bi-stability and reconfigurability. In addition, we introduce a 3D combination of star-shaped units with zero effective Poisson’s ratio in three orthogonal directions allowing its behavior in each loading direction to be programmed independently. The mechanical instability of this metamaterial in each orthogonal direction directly depends on the characteristics of star-shaped units aligned in that direction. Also, our study provides a framework to program the star units and create the desired properties in each orthogonal direction of the 3D metamaterial.   

Topological defects in complex mechanical metamaterials

While topological defects play a crucial role in condensed matter, they are not widely explored in mechanical metamaterials. We introduce a systematic strategy to design frustrated metamaterials with local or topological defects. We uncover their distinct mechanical signatures, and show how defects can be harnessed to engineer a desired response. Our work presents a new avenue to systematically introduce frustration and defects with a topological signature in mechanical metamaterials.   

Propagation of Pop-ups in Kirigami Shells

Kirigami-inspired metamaterials are attracting increasing interest because of their ability to achieve extremely large strains and shape changes via out-of-plane buckling. While in flat kirigami sheets all ligaments buckle simultaneously leading to a continuous phase transition, here we demonstrate that kirigami shells can also support discontinuous phase transitions. Specifically, we show via a combination of experiments, numerical simulations and theoretical analysis that in cylindrical kirigami shells the buckling induced pop-up process initially localizes near an imperfection and then, as the deformation is increased, progressively spreads through the structure. Notably, we find that the width of the transition zone, as well as the stress at which propagation of the instability is triggered, can be controlled by carefully selecting the geometry of the cuts and the curvature of the shell. Our study significantly expands the ability of existing kirigami metamaterials and opens avenues for the design of the next generation of responsive surfaces, as demonstrated by the design of a smart skin that significantly enhance the crawling efficiency of a simple linear actuator.   

Kirigami surfaces: programmable mechanical response via hierarchical design

Kirigami - the ancient Japanese art of cutting paper - has recently inspired the design of highly stretchable and morphable mechanical metamaterials that can be easily realized by embedding an array of cuts into a thin sheet. An attractive feature of these systems is that they are manufactured as a simple flat surface with cuts and then exploit elastic instabilities to transform into complex three-dimensional configurations. In this study, we focus on a thin elastic sheet perforated with a hierarchical pattern of cuts and demonstrate that the hierarchy significantly enhances the programmability of the system. In particular, we show that, by tuning the geometric parameters of this hierarchy, not only a variety of different buckling-induced 3D deformation patterns can be triggered, but also the stress-strain response of the surface can be effectively programmed. Finally, we show that when multiple hierarchical surfaces of various geometric patterns are brought together to create one combined heterogenous surface, the mechanical response can be further tuned and complex stress-strain curves can be achieved.   

Nonlinear elastic response of a topological mechanical metamaterial

We consider the static response of a finite 1D lattice of pivoting rigid bars connected end-to-end by harmonic springs of zero equilibrium length. The linearized model is equivalent to the Kane-Lubensky model of rigid rotors and is topologically polarized when the pivot point of each bar is off center. We fix the angular displacement of the leftmost bar and solve the nonlinear torque balance equations for the equilibrium configuration. For the unpolarized case, we find an algebraic decay of the rotation angle θ_n due to nonlinear effects associated with the bulk zero mode. For one sign of the polarization, θ_n decays exponentially and the elastic energy is nearly zero, consistent with the excitation of the zero mode at the left edge. For the other sign, θ_n also decays exponentially with the same decay length as the zero mode, but with a finite energy, and there is a turning point beyond which θ_n grows exponentially toward the free boundary. Numerical solutions are explained in detail by an analysis that necessarily includes terms of up to fifth order in θ_n. The results provide insight into numerical results for the directional response of a 2D mechanical graphene model to an externally applied local strain.   

Geometric information and rigidity percolation in floppy origami

Floppy origami structures have many folded configurations and are thus natural candidates for storing information geometrically. To address how we might harness this idea, we study the effect of folds and constraints in a planar tessellation inspired by the simplest globally coordinated origami pattern known as Miura-ori. Introducing folds randomly along the diagonals of the quads in Miura-ori makes the rigid structure floppy. We show how the number of degrees of freedom in the system varies with the increase in the density of constraints, first linearly, and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via an inherent redundancy that depends on the assignment of constraints, and the degrees of freedom in the system depends on the density of constraints in a scale-invariant manner. The redundancy in the constraints shows a percolation transition at a critical constraint density $\rho_c$. Our work shows how floppy origami can be used to store information in a scale-invariant way, and how we can control its rigidity exquisitely by taking advantage of a percolation transition.   

Topological Directional Response in the Continuum Limit of Mechanical Metamaterials

Flexible mechanical metamaterials display an exciting variety of novel deformation properties, including programmability, nonlinearity and robustness. However, these functionalities, which rely on nonuniform deformations of the microscopic unit cell of which the metamaterial is composed, are not captured by conventional elastic theory, creating a challenge in examining their actual large-scale properties. We address this via micromorphic continuum elasticity, which treats deformations that are nonuniform locally yet vary smoothly over larger lengthscales. We examine in particular topological edge and interface modes and directional response analogous to that observed by Kane and Lubensky in discrete models. We identify a new counting argument between modes of deformation and constraints that ensures mechanical criticality in the continuum, leading to a novel correspondence between a bulk topological invariant and boundary modes. Finally, we explore the lengthscales of deformations governed by this theory for given system geometries, elastic properties and disorder.   

Topological edge floppy modes in quasicrystals

Quasicrystals (QCs) are fascinating materials that exhibit physics properties not available in crystals, such as rotational symmetries forbidden in lattices, physics of higher dimensions, and self-similarity. The interplay of these unique features with topological states of matter can offer a rich variety of interesting phenomena. In this talk, we discuss topological mechanics in 2-dimensional quasicrystalline parallelogram tilings. We use the Penrose tiling as our example to demonstrate how these boundary modes arise with a small geometric perturbation to the tiling. The same construction can also be applied to disordered parallelogram tilings to generate topological boundary floppy modes. We find that, due to the unusual rotational symmetry of quasicrystals, the resulting topological polarization can exhibit orientations not allowed in periodic lattices. Our result reveals new physics about the interplay between topological states and quasicrystalline order and leads to novel designs of quasicrystalline topological mechanical metamaterials.   

The topological basis of function in flow and mechanical networks

Recently, both flow networks and mechanical networks have been shown to be remarkably tunable. By tuning the local node connectivity, it is possible to robustly control the propagation of inputs in order to achieve a wide variety of specific tasks. However, the network architectures used to achieve such tasks demonstrate significant design flexibility, blurring the relationship between structure and function. Here we seek to identify the structural features responsible for function in tuned networks. Using persistent homology, we show that networks develop large-scale topological features when they are tuned, which are similar for different networks with the same function, regardless of the details of the local link topology. These features correlate strongly with the tuned response, providing a clear relationship between structure and function.   

Using tunable origami for active energy absorption

Energy absorption devices are widely used to mitigate damage from collisions and impact loads. Due to the inherent uncertainty of possible impact characteristics, passive energy absorbers with fixed mechanical properties are not capable of serving in different application scenarios. Therefore, origami-inspired structures, which possess the ability to reconfigure and deploy, are a qualified candidate for a novel active design. In this work, we apply the constrained zipper-coupled Miura-ori tubes (deployable and stiff after locking) as the basis to a tubular energy absorber. Numerical and experimental (static and dynamic) studies are performed to quantify the response of these novel structures. This work shows that the reconfigurable origami could change their stiffness and the total amount of energy they absorb. These behaviors are suitable for creating systems with on-demand properties that adapt to different impact scenarios.   

Atomic layer deposition for membranes, metamaterials, and machines

Ultra-thin films of inorganic materials are well-suited for fabrication of micron-scale actuators because they can sustain small radii of curvature, are compatible with semiconductor processing, and are chemically robust. We leverage atomic layer deposition (ALD) to produce free-standing mechanical devices with sub-5 nm film thicknesses. We fabricate cantilevers from ALD films to characterize the mechanical properties. We find that ALD films are elastic and exhibit a bending stiffness on the order of 10^-15 J. These measurements enable fabrication of cantilever springs with ultra-low spring constants suitable for micron-scale machinery. ALD mechanical metamaterials are fabricated by patterning of both the film and its substrate. Corrugations transferred into the ALD film enhance its bending stiffness and enable bending anisotropy, while cuts etched into the film soften the in-plane response. We integrate these results to produce magnetically actuated three-dimensional devices with applications in micromachinery.