Symposium CP07—From Mechanical Metamaterials to Programmable Materials

We present micron sized self-folding structures that consist of nanometer-thin, atomic layer deposited SiO₂-Si₃N₄ bilayers, built with conventional semiconductor fabrication methods. A bending response originating from strain differentials within these bilayer stacks is used for bidirectional fold actuation. 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.

Reconfigurable soft metamaterials that can bend, fold, or transform the shape in response to external stimuli have attracted significant interests in design of actuators, sensors, and smart materials and devices. We fabricate a variety of periodically ordered, porous membranes with different size, shape and arrangement from responsive polymers, including poly(dimethylsiloxane) (PDMS), poly(2-hydroxyethyl methacrylate) (PHEMA) based hydrogels, and shape memory polymers (SMPs). By exploiting mechanical deformation in these material systems in respond to environmental cues, such as pH, heat, light, and mechanical stretching, we investigate pattern transformation, auxetic properties, and programmed deformation for penitential . We further design and synthesize nematic liquid crystal elastomers (LCEs), two-way SMPs, with large and anisotropic strains, and precisely align the monomers and oligomers within the patterned microchannels. In turn, we demonstrate pre-programmed folding of 2D sheets into 3D with various curvatures.

Additive manufacturing of structures capable of changing their properties or shape in a programmed controlled manner is a booming research field. A large number of studies show that the unique capabilities of 4D printing (freedom of geometrical design space and locally controllable material in combination with active materials) enable the development of structures with completely new properties, e.g. programmable mechanical or thermal response and shape transformations.
This new way of fabrication is particularly of interest in the field of origami. Origami-inspired structures can be used in deployable structures, where a minimum amount of storage volume is desirable. Further, studies show that two dimensional origami patterns can be assembled into three-dimensional metamaterials, capable of changing their properties. Conventional fabrication of these structures often requires assembly and joining limiting the achievable designs. This can be overcome by an additive manufacturing approach, which allows the fabrication highly complex origami structures in a one-shot process.
Seemingly, the only limitation for these newly presented structures is the imagination of the engineer. In reality, structures finding their way into real life applications are an exception. The reason for this gap between laboratory scale and industry are the to-date insufficient mechanical properties. Usually loading capacity and fatigue resistance of the hinges are insufficient for the requirements imposed by possible applications. This holds particularly true for living hinges. 3D printed pin joint designs usually require much larger dimensions compared to living hinges. For the majority of the origami structures this is not feasible.
This study addresses these limitations of 3D printed origami-inspired structures. We focus on the characterization and optimization of the mechanical properties of 3D printed living hinges, including strength, bending stiffness and fatigue. This often-disregarded aspect is essential for pushing the existing origami-inspired structures further towards real life applications. We introduce a new type of 3D printed hinge, fabricated by multi-material FDM printing using continuous fibers. These composite hinges show large potential to significantly improve the loading capacity of the existing structures. Other hinge designs investigated are multi-material hinges fabricated by ink jet printing of photo-curable polymers and single material hinges printed by FDM from common 3D printing materials. The influence of design parameters such as cross section area and length of the hinge, as well as number of loading cycles, on the mechanical properties are investigated. Mechanical characterization of the hinges show tremendous difference in the loadbearing capacity. The maximum tensile load of composite hinges are up to two orders of magnitude larger than the one of inkjet printed multi-material hinges. Finally, maps correlating mechanical properties with design parameters are developed as a tool for selection of manufacturing technology, material and design of hinges for desired combinations of bending stiffness and loading capacity tailored to given applications. This work represents a first step towards bringing the advances in the field 3D printed origami-inspired structures closer towards application.

Additive manufacturing has greatly expanded the design space for mechanical metamaterials. This increased freedom has however identified the need for a systematic methodology to allow one to select a design solution from a range of infinite possibilities. Specifically, one needs to address four important questions when designing structures with cellular materials: (1) what is the optimum metamaterial unit cell shape?; (2) how should the size of these cells vary spatially?; (3) what is the optimum set of local parameters (such as thickness) and how do they vary spatially; and (4) how should the metamaterial be integrated within the larger structure?

In this presentation, we focus on the first question, that of selecting a metamaterial for a specific structural (mechanical) application. While recent advances in commercial design software have enabled the optimization of parameters in response to local stresses, shape selection is largely left to the designer's discretion. There have been some attempts in the literature to find optimum mechanical materials under simple loading conditions. However, it is not evident that these metamaterials retain their optimality in the context of more complex loading conditions such as those in realistic engineering structures. To address this challenge, we studied the deformation response of a beam comprised of various metamaterial shapes, under four different loading conditions: bending and torsion, in addition to tension and compression. As a comparative baseline, we also studied the same problems using topology optimization methods where the optimization operates at the level of the entire structure, as opposed to locally at the level of the individual cell.

To enable meaningful comparisons between these different approaches and geometries, we use a geometric efficiency index specific to each loading condition (e.g. flexural rigidity for bending) and show how it may be used to make design decisions to select among multiple cellular shapes with the intent of minimizing mass. This approach has the added advantage of allowing the designer to isolate the effect of composition ("bulk" material property) from geometry (metamaterial design) and thus draw conclusions with potentially wide applicability across different materials. Development of such indices for different shapes under a range of loading conditions may in the future enable a designer (or a software tool) to assign a metamaterial locally in response to the stress state at that specific location.

The performance of porous materials with low relative density is limited by buckling of struts or cell walls, which reduces strength and energy storage during large deformations. Motivated by the expanding design space accessible via additive manufacturing, this paper examines the efficacy of combining multiple cell shapes and variable strut sizes to control buckling and improve compression response. A simple V-shaped cell between rigid platens is divided into sub-cells using smaller internal braces that run perpendicular to the loading direction (trapezoidal sub-cells) or at inclined angles (triangular sub-cells). Finite element simulations with linearly elastic beam elements that account for large rotations and self-contact are used to predict performance at fixed relative density. A broad parameter study will be illustrated showing the impact of sub-cell shape and strut size. Despite the simplicity of the structures, the simulations illustrate complex relationships between topology and post-buckling behavior that arise from highly non-linear kinematics. This complexity has important implications for the topology optimization of large deformation response of cellular solids. While performance can be highly sensitive to sub-cell geometry, the overall trends demonstrate that triangular sub-cells with small cross-sections (relative to the main V-struts) are effective in suppressing lower order buckling modes. Such structures exhibit improvements in peak stress and elastic energy storage of a factor of two or more, relative the undivided V-cell. The implications for designing low density materials are briefly discussed.

Reconfigurable structures with tunable mechanical and functional response can enable dynamic functionality to improve performance and enhance versatility of materials and systems. One promising approach to create such structures is through the use of patterned folds or cuts in initially planar materials. Kirigami, the Japanese art of paper cutting, has demonstrated that the inclusion of cut patterns enables complex 3D structures from 2D sheets, elastic softening, and large deformations under external loading. Here we present reconfigurable and multistable mechanical metamaterials through the coupling of non-linear structural deformations with material non-linearities. First, we generate fabrication approaches to combine multiple material sets into a single material system through the combination of rapid prototyping through laser cutting and soft lithography. We then perform mechanical experiments to investigate the material and structural non-linearity upon deformation. Experimental results are supported by theoretical predications and simulations, which relate the material stiffness and deformation characteristics to the material composition and geometry. By tuning these parameters, we create 2D films which are capable of morphing into complex 3D shapes and then being electrically triggered to return to the initial 2D state. This work can enable substantial variations in stiffness and deformation of functional materials for applications in soft robotics, stretchable electronics, and human-machine interfaces.

Ordinary materials neither exhibit multi-stability nor chiral mechanical response. This means that they cannot be stabilized in multiple conditions and that they do not convert stretch into twist. In contrast, metamaterials give access to such behavior. The design of such metamaterials to specific materials properties requires mechanistic materials modelling over multiple length scales to avoid tedious trial-and-error procedures and excessive experimentation.

Concerning chirality, Frenzel et al.[1] have created a chiral mechanical metamaterial and successfully mapped its behavior onto a micropolar continuum which predicts that the magnitude of the twist must decrease inversely proportional to the ratio of the sample size to the size of one unit cell. To create chiral response for larger samples, the decay of the twist must be pushed to larger scales or eliminated. We first combine chiral unit cells with non-chiral coupling elements to form binary crystal structures exhibiting ultra-long decay-lengths compared to previous three-dimensional chiral mechanical metamaterials. We then proceed to generate structures that completely avoid this decay.

Multi-stability can be achieved with metamaterials that contain elastic buckling elements[2,3]. Gradients in the metamaterial in principle give access to a quasi-continuous regime of mechanical properties. Such graded metamaterials can be designed such that their effective materials properties can still be dramatically changed after manufacturing. I will take this as an example for an intrinsically programmable material. While the deliberate adjustment of locally different materials properties in a component may be regarded as the programming of a material to achieve component functionality, intrinsically programmable materials will allow realizing complex system functionalities including sensor and actor functions.

[1] T. Frenzel, et al., Science 358 (2017) 1072
[2] T. Frenzel, et al., Adv. Mater. 28 (2016) 5865
[3] C. Findeisen, et al., JMPS 102 (2017) 151

One of the many potential applications of mechanical metamaterials is in the design of energy absorption structures used in functional components such as helmets and automotive crash structures. Traditionally, these structures have been manufactured using stochastic foams, but Additive Manufacturing (AM) process technologies have enabled the design of metamaterials with tailored and locally modified properties. The vast majority of literature on AM metamaterials for energy absporption have typically focused on the identification of a metamaterial unit cell shape that is optimal for energy absorption. In this work, we report on an alternative approach we have explored to incorporate "negative space" around metamaterials into the design of energy absorption structures.

The ideal energy absorption structure meets two objectives simultaneously - it provides high energy density, while also keeping the maximum transmitted stress to a low value. The former requirement ensures energy is absorbed with as little material as possible, which is important from a packing (in the case of a helmet) or light-weighting (in the case of an automotive crash structure). The objective of reducing the maximum transmitted stress is to keep the occupant safe and isolated from the effects of the stress.

In this work, we borrow the concept of "negative space" from the world of art, where it is typically used to describe the space around the subject. In art, negative space is often most evident when the space around a subject, and not the subject itself, forms an interesting or artistically relevant shape, and such space occasionally is used to artistic effect as the "real" subject of an image.

We used this concept to introduce negative space into a regular, periodic square honeycomb design with the intent of studying its effects on the mechanical properties of these honeycombs under compression. Our key finding in this work is that the introduction of negative space, particularly in the form of spiral patterns or as non-collinear spaces can significantly increase the energy density for a given maximum transmitted stress. This data is collected using additively manufactured polymer honeycombs tested under compression. We leverage this empirical data to develop design principles that may be integrated into energy absorption structures more generally. While this work is limited to prismatic honeycombs, it is in principle, extendable to 3D metamaterials. On a more abstract level, we suggest that it is negative space, and not the metamaterial itself that may be functionally relevant for energy absorption and peak stress minimization, or at least play a complementary role along with the identification of an ideal metamaterial.

The fundamental problem of how structure scales and size-dependently impacts materials has occupied humanity for centuries. Modern manufacturing techniques now allow us to investigate this basic question with incredible freedom, and rational design approaches to the structuring of materials can result in metamaterials with unique properties. A scale-bridging understanding of how structure defines such a metamaterial independent of its base composition is necessary for this rational design process to be successful. Herein we examine metamaterials with a view spanning their internal ‘mechanisms’, the unit cell, its connectors, and finally the resultant matrix with its hierarchically subordinate components. Some recent efforts in the development of programmable mechanical metamaterials, or designed materials that respond to external stimuli in a discrete and ideally reversible fashion, will be presented that rely on a clear understanding of rational hierarchical design approaches.

From the current perspective, there is little room for further expansion of the accessible material property space by classical material fabrication methods. Single one- and two-dimensional nanoscale objects, such as nanowires and thin films, are known to hold exceptional physical properties. Yet, their properties are intrinsically coupled to their small size and their solitary nature, and therefore can hardly be accessed in actual materials of practical volume. If nanowires and thin films are simply scaled up properties, which relate to surface to volume effects, get lost, when clustered in a composite interfaces dominate the overall performance. Nanoarchitected metamaterials are regular three-dimensional networks constructed from nanowires or thin films and have the potential to overcome such limitations. Two-photon polymerization (TPP) is the most versatile technology for fabricating nanoarchitected metamaterials and rapidly progresses towards higher throughput, resolution and a broader spectrum of printable materials. However, TPP fabrication is still largely empirical without systematic data on material properties and limited knowledge on their dependency on the process parameters.
In this work, we systematically characterized the mechanical properties of two-photon polymerized resins as well as corresponding pyrolytic ceramics, from nanowires to bulk specimens. We show that the properties of the material systems can be tailored from rubbery soft to hard and strong, and explain the observed behavior by a photonics-based model allowing to predict the mechanical properties of two-photon polymerized materials depending on applied process parameters. In a second step we incorporated specifically designed material properties in different nanoarchitected metamaterials. We discuss the interplay of material design approaches, size-effects and different topological designs and show unique effective characteristics such as mechanical performance at the theoretical limit of both the architecture and the constituent material.

I will present a transformative idea of designing meso-structures (termed as meta-grains, meta-precipitates and meta-phases) that imitate key microstructures (namely crystal grains, precipitates and phases) in crystalline metals to generate a new type of meta-materials: meta-crystals. This mimicry enabled by additive manufacturing opens a unique opportunity to employ the key hardening mechanisms found in metallurgy to the design of architected materials. This study demonstrates that such meso-structures play the same roles on governing the properties of meta-crystals as do intrinsic microstructures in metallic alloys, opening up a new space of designing lightweight and damage-tolerant materials with desired properties.

Mechanical meta-materials that mimic the crystal lattices are lightweight and hold great potential for a wide range of applications, such as aerospace, automobiles and medical devices. However, previously reported lattice meta-materials consisted of lattices that are singly oriented. Such lattice meta-materials are analogous to single crystals, and normally exhibit unstable deformation behaviour due to the occurrence of single shear bands throughout the whole lattice, resulting in substantial reduction in energy absorption. In this study, we present a novel approach to mimic the polygrain structure in metallic alloys and bring the grain-size hardening effect in polycrystals to develop polycrystal-like meta-materials. We found that the boundaries separating meta-grains play an influential role in the propagation of shear bands in the same way as the grain boundaries do in slip activities in metals. Most interestingly, the strength of polycrystal-like meta-material is found to increase with decreasing the size of meta-grains, similar to the Hall-Petch relationship. Moreover, this talk will demonstrate that we can engineer the crystal-like lattice structures to tune the meta-material properties in the same way as the microstructure engineering in metallurgy. The tailoring of anisotropy of meta-materials will be presented as an example.

Three-dimensional lightweight material building blocks, through the combination of molecular design of material behavior and microscale geometric patterning, show promise to revolutionize the ability to dissipate energy and manipulate wave propagation. Such materials are desirable for a broad array of applications such as structural components, catalysts supports and energy efficient materials.

In this invited talk, I will present our development of three dimensional micro/nanofabrication technique, projection microstereolithography (PuSL), to enable design and exploration of digitally coded multifunctional and multimaterial lightweight metastructures at unprecedented dimensions. The ultra-high resolution and multi-material capabilities of the 3D printing system and the modeling tools developed can be used to design and fabricate architected materials for combined functions, including energy absorption, actuation/morphing, and reactors with fast thermal response and efficient convection of working fluids. I will also discuss the development of engineered, three dimensional arrays of copolymer fibers that serve as mimetics of neuronal axons, using a combination of materials engineering and high resolution 3D microfabrication, which enable study of OPC engagement and subsequent myelination in vitro.

Multiphoton lithography is the widely used 3D micro-printing method that enable fabrication of architected microstructures in length scales of 1um. However, the further reduction of the feature size and the printing of curved surfaces still remain challenging. Here we report that the focused laser beam can induce localized pyrolysis on polymer-ceramic hybrid architected metamaterials. The minimum feature size is reduced from 400nm to 250nm, yielding a volume reduction factor of 2.56. With nanoindentation experiments, we confirmed that a top-down z-dependent deformation on the architected metamaterial introduces an 100% enhancement in mechanical strength. Additionally, in-plane 2D xy-dependent deformation generates controllable curved surfaces from straight lattice struts. Hence, the laser induced site-selective deformation offers on-demand modification of the physical geometry and mechanical properties for architected metamaterials.

Ultra-thin films of inorganic materials are well-suited for fabrication of micron-scale actuators because they can sustain small radii of curvature, have large force outputs, are compatible with semiconductor processing, and are chemically robust. We leverage atomic layer deposition (ALD) on sacrificial substrates to produce micron-scale free-standing mechanical devices with sub-10 nm film thicknesses. We fabricate cantilever springs from ALD films and characterize the material’s mechanical properties. We find that ALD films are remarkably elastic and exhibit a bending stiffness on the order of femtojoules. These measurements enable fabrication of cantilever springs with tailorable ultra-low spring constants suitable for micron-scale machinery. The mechanical properties of ALD are further modified by lithographic patterning of both the ALD film and its substrate in the design of mechanical metamaterials. Substrate corrugations transferred into the ALD film enhance its bending stiffness and allow programmable bending anisotropy, while lattices imposed into the film decrease its effective Young’s modulus for stretchable and auxetic materials. We integrate these results and device concepts to produce magnetically actuated three-dimensional structures with applications in micromachinery. Our results establish thin ALD films as a scalable basis for micron-scale actuators and shape-programmable microrobotics.

Fused deposition modeling (FDM) is an additive manufacturing (aka 3D printing) process that extrudes viscous material in 1-dimensional lines to create 2-dimensional layers that build up to a 3-dimensional part. The creation of magnetic composite parts is just beginning to be explored with FDM. Previous work has found the out of plane direction (perpendicular to the print plane) to be a magnetically hard axis. This motivated further investigation into the influence of specific print parameters on the magnetic properties of parts, as this has not yet been fully characterized. The ability to mechanically manipulate materials via magnetic fields (such as magnetic shape memory alloys, magnetostrictive materials, and magnetorheological materials) means that tailoring the magnetic properties of such materials is intimately tied to tailoring their performance over time (i.e. 4D-structures). Here, we explore this topic with a composite magnetic filament consisting of PLA (polylactic acid) polymer and 40wt.% iron as a step towards constructing 3D-printed structures where the magnetic response is “programmable”. This filament was used in an FDM process to print magnetic samples of varying length, width, infill percentage, and infill print orientation. The length and width variables resulted in parts of two different macroscopic dimensions: 5mm by 10mm (anisotropic) and 10mm by 10mm (isotropic), both with a height of 2mm. The infill percentages printed were 60%, 70%, 80%, 90%, and 100%. The infill print orientation refers to the direction the printer extruded the 1D filament in order to create the part shape, either along or against the shape anisotropy. From these variables, and since the square samples required only one set of prints to get both print orientations due to symmetry, there were 12 unique parts. Three of each were printed, resulting in a total of 36 parts that were tested. A vibrating sample magnetometer (VSM) was used to determine the effect of these different print structures on the magnetic response to a maximum applied magnetic field of 1.4 T. Hysteresis loops for each sample were measured with the magnetic field applied along the longitudinal and transverse directions of the part, resulting in 72 total tests. This data was used to compare the magnetic susceptibilities between the different print structures. After preliminary testing, all parts were tested again for consistency of procedure and data acquisition. The results show that infill orientation has a prominent effect on the magnetic properties. At lower infill percentages, magnetic susceptibility is greater parallel to the infill orientation. This phenomenon is also seen for the samples with anisotropic shape, showing that the susceptibility along the long axis of a part but perpendicular to the infill orientation is lower than that of the susceptibility along the short axis of a part but parallel to the infill orientation. However, as infill percentage increases, this effect diminishes, and the effect of the macroscopic shape then has an equal effect on magnetic susceptibility as the infill orientation. The infill orientation anisotropy effects are reduced at higher infill percentages due to the minimization of air gaps that magnetic flux lines must traverse going through the sample. Determining how shape, infill orientation, and infill percentage affect the magnetic properties of printed parts will help in understanding how an FDM process can be developed to “program” these properties in order to manipulate the mechanical performance of 4D-materials, incentivizing FDM as a method for manufacturing magnetic components.

Stimuli sensitive polymers that swell in response to interaction with various solvents offer possibilities to achieve controllable shape transformations. Temporal interaction of these materials with solvent, when controlled locally, can be translated into programmable shape modulation.^1–3These geometrical transformations occur over a time scale that depends upon the solvent and the material properties, as well as the size/shape of the material and thus can be easily controlled.⁴Here, we use coupled experimental and theoretical methods to quantify geometry dependent shape transformations of rubbery materials that are locally subjected to a train of solvent droplets. Based on relative comparison between diffusion time scale and droplet pulse period, we identify regimes where such shape transformations can be achieved and controlled. This regime is achieved when the two timescales are comparable whereas equilibrium swelling occurs at the two extremes of this scaling. To demonstrate the various regimes, we study swelling of six cylindrical geometries of PDMS with varying aspect ratio subjected to pulsating drops of n-hexane. As a result, a localized swelling feature incremental in time and space domain is observed. Furthermore, we show that the characteristic of this swelling feature depends strongly on the sample aspect ratio relative to the droplet size. We demonstrate this using two cases of cylindrical geometries and a custom finite element model. We use this validated model to predict the geometries of rest of the cases and show dependence of characteristic swelling feature on sample aspect ratio. These deformations are magnified during the droplet-train impact but dissipate during post-train polymer equilibration. Our results also show that while swelling shape is a function of lateral dimensions of the sample, with the extent of swelling increases with the elastomer sample thickness.⁵
References:
1. Holmes, D. P. et al.Bending and twisting of soft materials by non-homogenous swelling. Soft Matter7,5188 (2011).
2. Stoychev, G., Zakharchenko, S., Turcaud, S., Dunlop, J. W. C. & Ionov, L. Shape-programmed folding of stimuli-responsive polymer bilayers. ACS Nano6,3925–3934 (2012).
3. Lee, H., Zhang, J., Jiang, H. & Fang, N. X. Prescribed pattern transformation in swelling gel tubes by elastic instability. Phys. Rev. Lett.108,1–5 (2012).
4. Holmes, D. P. & Crosby, A. J. Snapping surfaces. Adv. Mater.19,3589–3593 (2007).
5. Phadnis, A., Manning, K. C., Sanders, I., Burgin, T. P. & Rykaczewski, K. Droplet-train induced spatiotemporal swelling regimes in elastomers. Soft Matter14,5869–5877 (2018).

It is inevitable that structures including bridges, pipelines, and aircraft eventually develop cracks. Unfortunately, current design practice does not include the means of structural damage detection into the design process. In this paper, periodic superstructure and substructure are induced at pre-design and post-design processes in order to control dynamic response of structure and generate local resonators and redirect/control elastic waves, respectively. For the pre-design process, various truss topologies are configured with a periodic pattern for monitoring their variations with localized damage using the impulse response method independent from boundary conditions. For the post-design process, the presence of damage is monitored by Structural Health Monitoring (SHM) methods. Among many SHM methods, Acoustic Emission (AE) method has advantages of being non-intrusive, direct assessment of damage and localization. The major disadvantage of AE method is the sensitivity to background noise. Two-dimensional phononic crystal (PC) is designed to block unwanted background noise such that single AE sensor becomes sufficient to monitor the active flaws such as fatigue crack and corrosion. The other application of applying acoustic metamaterials to structural systems is the isolation of building superstructure from any dynamic loading through periodic substructure design with the band gap range of dynamic signal. The integration of periodic systems and acoustic metamaterials brings unique characteristics to the long term durability and resilience of infrastructure systems.

Additive manufacturing opens up a new design space to create architected materials with exotic properties not attainable by conventional materials – for example, negative refractive index, simultaneous ultra-high stiffness and recoverability, and photonic and phononic bandgaps. External stimuli like mechanical forces, wetting and dewetting, and magnetic field could be applied to reconfigure the structure of architected materials in order to achieve novel functionalities. Such transformations are usually binary and volatile because they toggle between the “on” and “off” states and require persistent external stimulus to stay in the deformed geometry. In this work, we demonstrate the cooperative beam buckling phenomenon that transforms a Si-coated tetragonal microlattice into an ordered sinusoidal lattice via electrochemically controlled Si-Li alloying reaction. Ex situ scanning electron microscopy reveals the stable structural transformation across multiple length scales from the nanostructured beams to the millimeter-scale bistable domains. In situ optical microscopy visualizes the dynamic cooperative buckling process caused by lithiation-induced Si volume expansion and built-in mechanical instabilities in the lattice architecture. Long-term electrochemical cycling shows buckling and unbuckling of the lattice beams are highly reversible within a voltage range.
We investigate the mechanical dynamics of individual buckling beams and the cooperation of buckling directions among neighboring beams using a coupled chemo-mechanical finite element model, which highlights the interplay between large elastic-plastic deformation and instability-driven buckling. Furthermore, we discover the stochastic distribution of local defects in architected materials play an important role in the formation of domains separated by distorted domain boundaries and analyze such phenomenon with a statistical mechanics model analogous to the Ising model. Our study provides a pathway for predicting dynamic architected material responses according to defect density and distribution, which has not been discussed in previous works. With this understanding, we designed and implanted artificial defects in Si microlattices to deterministically control buckling directions to produce single-domain sinusoidal lattices and to program domain boundaries that form a particular pattern. This new class of electrochemically reconfigurable architected materials provides insights for next-generation battery electrodes with novel stress-relief mechanisms and dynamic mechanical metamaterials with tunable phononic bandgaps.

Metamaterials are experiencing a resurgence in engineering application on account of Additive Manufacturing (AM) since it is now increasingly possible to manufacture complex geometries that include these structures. Manufacturing parts with mechanical metamaterials have several advantages: lower material and energy utilization in the manufacturing process as well as lifetime savings due to the product’s higher performance, especially in weight sensitive domains such as transportation (ground, air or space).

Despite the significant potential of combining metamaterials with AM, there has been limited implementation in end-use functional parts. A key challenge to realizing this goal stems from our inability to model and predict metamaterial behavior reliably. This is on account of several relatively well-understood reasons including sensitivity to geometric tolerances and microstructure variation at small scales. In this work however, we focus on an aspect of characterizing and modeling metamaterials that has not received enough attention in the additive manufacturing literature, and that is the fact that these materials are highly sensitive to strain rate. This is true at “quasi-static” strain rates, and not just at the higher strain rates associated with impact. We examine the underlying reasons for this, showing how local strain rates can significantly exceed those applied globally.

To simplify our ability to characterize and model observed behavior, we limit our study of strain rate dependence to hexagonal honeycombs across four different additive manufacturing processes: one polymer (Fused Deposition Modeling with ABS), one composite (Nylon and Continuous Carbon Fiber Extrusion) and two metallic (Laser Powder Bed Fusion of Inconel 718 and Electron Beam Melting of Ti6Al4V). We compare strain rate sensitivities of the effective elastic modulus and peak load for all four processes. We also report on strain rate sensitivities for the polymer honeycombs for five different shapes: hexagonal, square, triangular, Voronoi and for a graded structure that induced buckling failure. In all cases, significant strain rate sensitivities were observed from applied nominal strain rates ranging from 1 to 10^-6 s^-1. Finally, we use beam theory and Finite Element Analysis to model this strain rate dependence for the polymeric material and show that the inclusion of strain rate dependence is essential for the accurate elastic-plastic modeling of honeycomb deformation. This study has implications for the characterization and modeling of all mechanical metamaterials and suggests that accurate representation of these structures must include strain rate effects.

Mechanical metamaterials exhibit enhanced properties derived from their architecture. Advances in 3D printing techniques have enabled the fabrication of complicated designs even at the microscale, contributing to the progress of state of the art ultra light materials with superior mechanical features. Nevertheless, comprehending the mechanism of strain hardening that is an inherent characteristic to the structure and arrangement of the unit cells is rather limited and fairly empirical. In this study, we present a novel design of mechanical metamaterial structures influenced by the first stellation of rhombic dodecahedron, and juxtapose its mechanical behavior with one of the most meticulously studied metamaterial designs, the octet truss and its counterpart bulk material. The uniqueness of the present design is the adaptation of crystal twinning in a two-level design process of the unit cells, that is, the architecture of unit cells and their connection to adjacent unit cells. Our findings validate that this design strategy is highly efficient in enhancing the metamaterial’s strength and energy adsorption potential, while simultaneously diminishing the volume occupied by the structure considerably. By performing simulations and nanoindentation tests for these metamaterial structures fabricated by two-photon lithography, we have proven that this new type of metamaterials surpasses both the bulk material and the octet truss structure, as indicated by the remarkably higher strain hardening and energy dissipation characteristics obtained for the same deformation, despite the significantly smaller volume of the first stellation structure. Our study introduces a novel design technique for controlled strength and strain hardening in mechanical metamaterials by the strategic placement of simple platonic solids to form more complex structures with deformation modes resembling those of microlattices that exhibit crystal twinning.

Wave manipulation using artificial materials is a central topic in materials physics. Recent years have witnessed the emergence of a family of thin, 2D artificial materials, namely, metasurfaces. The concept of metasurfaces was introduced to the materials and physics communities for optical waves in 2011 with the generalized Snell's law, which opened up a new degree of freedom for optical wave manipulation. Inspired by this pioneering work, and because acoustic waves also follow the Snell's law, a flurry of activity has revealed acoustic metasurfaces for controlling sound and new applications in acoustics. However, mapping the success of electromagnetic metasurfaces to the acoustic domain is challenging, primarily owing to the intrinsic differences between electromagnetic and acoustic waves. In this talk, I will delineate the underlying fundamental physics of metasurfaces, describe their different concepts, the design strategy, and discuss their functionalities for controllable reflection, transmission, and extraordinary absorption. In particular, I will discuss our recent works on acoustic metasurface-based ultrathin sound diffusers and gradient-index metasurface-induced asymmetrical sound transmission.

Solid-state photochemical reactions in molecular crystals can generate large-scale motions and shape changes. These photomechanical crystals have potential applications as light-controlled actuators and smart switches. Micro- and nanocrystals can exhibit motions like bending, twisting, curling, and jumping under light illumination. However, controlling the size and shape of molecular crystals remains a challenge because the weak van der Waals intermolecular forces between organic molecules undermine their ability to lock in a specific shape during crystallization. Besides the overall crystal shape, the orientation of the molecules within that shape should also play an important role in determining the photomechanical response. In general, the arrangements of molecules in a crystal are determined during the early stages of crystallization process. Recently, our group developed a surfactant-assisted seeded growth method to prepare single crystal platelets composed of 9-methylanthracene (9MA) with two different internal molecular orientations in aqueous solution. The more stable form exhibits a photoinduced twisting motion and elongated hexagonal platelets undergo a photoinduced rolling-up and unrolling which can be used to wrap and translate magnetic nanoparticles with external magnetic field applied. What is more, we have extended our seed-growth technique to other anthracene derivatives. We had successfully grown uniform block-like microcrystals composed of cis-dimethyl-2(3-(anthracen-9-yl)allylidene)malonate (cis-DMAAM) in aqueous surfactant solutions. A brief pulse of light (< 405 nm) causes these crystals to undergo delamination (peeling). This peeling process can be repeated multiple times on the same microblock, uniformly peeling off layer after layer with a train of light pulses. Our results demonstrated how tuning crystal morphology (size and shape) can lead to novel modes of mechanical behavior. This novel crystal growth method generates new crystal shapes that illustrate the versatility of photomechanical molecular crystal materials.

Optical metasurfaces composed of designed Mie-resonant semiconductor nanoparticles arranged in a planar fashion offer unique opportunities for controlling the properties of light fields [1]. Such metasurfaces can impose a spatially variant phase shift onto an incident light field, thereby providing control over its wave front with high transmittance efficiency. They can also e.g. act as polarizing optical elements, exhibit tailored nonlinear optical properties, or manipulate spontaneous emission processes of nanoscale emitters integrated in the metasurface architecture. However, the optical response of most semiconductor metasurfaces realized so far was permanently encoded into the metasurface structure during fabrication. Recently, a growing amount of research is concentrating on obtaining dynamic control of their optical response, with the aim of creating metasurfaces with functionalities that can be programmed on demand.
This talk will provide an overview of our recent advances in actively tunable Mie-resonant semiconductor metasurfaces. In particular, by integrating silicon metasurfaces into a liquid-crystal (LC) cell, we can tune their linear-optical transmittance and reflectance spectra by application of a voltage [2]. Importantly, this tuning approach is highly compatible with established LC industrial technologies. We, for the first time to our knowledge, we utilize a LC photoalignment material [3] during the assembly of the LC metasurfaces, leading to a drastic improvement of the tuning performance and reproducibility. Based on this method, we demonstrate two electrically tunable LC-infiltrated dielectric metasurfaces working at near-infrared and visible wavelengths respectively. We show that these metasurfaces can be tuned into and out of the so-called Huygens’ regime of spectrally overlapping electric and magnetic dipolar resonances, which is characterized by near-unity resonant transmission, by application of an external voltage. In particular, we demonstrate tuning of the metasurface transmission from nearly opaque to nearly transparent at 1070 nm. Furthermore, making use of the strong modulation of the metasurface response in combination with patterned electrodes, we experimentally demonstrate a transparent metasurface display device operating in the visible spectral range. Finally, we propose a novel route toward phase-only tuning by applying simultaneous electrical and thermal stimuli to the LC-infiltrated dielectric Huygens’ metasurfaces.
However, while the integration of silicon metasurfaces into nematic LC cells represents an efficient and versatile tuning approach showing large resonance shifts and strong tuning contrast, the switching times that can be achieved based on this approach are limited. Thus, as an alternative tuning mechanism allowing for ultrafast operation, we consider the transient changes of the optical properties of semiconductor materials when optically pumped by femtosecond laser pulses. These changes can lead to pronounced changes of the resonance condition for semiconductor metasurfaces at an ultrafast time scale. This talk will review our recent progress in ultrafast switching and tuning of semiconductor metasurfaces based on different material platforms and different physical mechanisms occurring at an ultrafast time scale [4,5]. Furthermore, strategies to translate ultrafast tuning of metasurface resonances to ultrafast control of more complex metasurface functionalities such as wavefront shaping will be discussed.
[1] I. Staude & J. Schilling, Nature Photon. 11, 274 (2017).
[2] A. Komar et al., Appl. Phys. Lett. 110(7), 071109 (2017).
[3] I. I. Rushnova et al., Opt. Commun. 413, 179 (2018).
[4] M. R. Shcherbakov et al., Nano Lett. 15, 6985 (2015).
[5] M. R. Shcherbakov et al., Nat. Commun. 8, 17 (2017).