Session W21: Mechanical Metamaterials II

Designing 2D mechanical metamaterials with printability constraints using interpretable machine learning

Mechanical metamaterials present superior mechanical performance thanks to their designed microstructure. For instance, they can exhibit highly non-standard elastic behavior such as auxeticity or the formation of complete frequency band gaps. Recently, 3D printing has become a practical tool to realize such metamaterials that can be made out of multiple materials or even conveniently realized by printing a single material with voids within it. However, this latter approach introduces additional constraints that need to be considered, e.g., unit-cell connectivity.

We take elastic 2D metamaterials that exhibit band gaps as an example and discuss the application of interpretable machine learning to capture unit-cell features essential for opening band gaps within specified frequency ranges while also incorporating 3D printing considerations. Unlike conventional ‘black box’ machine-learning algorithms, interpretable machine-learning algorithms yield models that can be easily interpreted and checked. Thus, they offer an effective approach towards obtaining interpretable rules spanning the feasible design space (e.g., different unit-cell shapes and topologies) for complex problems, e.g, multi-classification problems or multi-objective problems involving multi-functional metamaterials.   

Non-contact Probing of Effective Elastic Constants in 3D Micro-Architected Materials

We present a non-contact characterization scheme for micro-architected materials that enables capturing the effective elastic constants as well as their linear dynamic response in a robust and iterative manner. In this work, micro-architected materials are fabricated using a two-photon lithography technique enabling feature sizes on the order of ~1 µm. To characterize their effective elastic constants, we induce photoacoustic stimuli in a pump-probe scheme to excite elastic waves in the architected materials and determine the modal response using a common-path interferometric setup. Through systematic tuning of the wave vector, we reconstruct the dispersion relations of the materials. We validate this technique using a variety of 3D architectures, and we compare our non-contact properties to those measured via classical nanoindentation techniques and computational homogenization models. This exploration merges expertise from ultrafast optics and metamaterial fabrication, elucidating a potential path for iterative and robust characterization of metamaterials in a dynamic regime. The findings could enable research opportunities for microscale metamaterials as phononic devices, or even provide a novel versatile approach to expedite mechanical-property explorations of the same.   

Additive Design of Origami and Kirigami

Origami and kirigami, the traditional paper folding and cutting arts, have become a paradigm for mechanical metamaterials in recent years. Previous studies on the design of origami- and kirigami-based structures have primarily focused on simple geometric constructions for limited spaces of origami and kirigami tessellations or global constrained optimization frameworks that are difficult to solve computationally. In this work, we present a novel additive approach for designing origami and kirigami structures. We begin with the smallest building block of origami and kirigami patterns and identify the geometric conditions for the compatibility of adjacent cells, and then move on to strips and finally surfaces. This simple marching construction allows us to create shape-morphing structures from flat sheets at any scale efficiently, and further enables the characterization of the entire design space of generic quad origami and kirigami patterns. Overall, our work opens up a new way for the computational design of shape-shifting structures.   

Harnessing imperfections to elicit functionality in soft mechanical metamaterials

Elastic instabilities, traditionally avoided in mechanical structures, have become a powerful tool to attain novel functionalities well-suited for a wide range of applications in soft robotics, smart structures, and logic devices. Existing studies are limited to exploiting elastic instabilities in periodic systems where the response can be inferred from the underlying defect-free representative volume element. In this work, imperfections in the form of soft inclusions are introduced in biholar metamaterials to control instabilities, thereby achieving tunable mechanical responses and programmable logic. Using a combination of numerical simulations and mechanical testing, we unveil the emerging mechanics and mechanisms that trigger instability and non-trivial non-linear responses. Programming location, density, and distribution of defects in soft biholar metamaterials enable to impart unique functionality that would be otherwise unachievable in their defect-free counterparts.   

Rayleigh-Plateau 3D printing of mechanical metamaterials for elastic bandgap tuning

In the last few years, the interest on mechanical metamaterials has increased significantly. This interest has pushed the usual manufacturing boundaries to simple, fast and accurate new techniques wich harness simple fluid mechanical properties towards robust mechanical ones. In our work we present mechanical metamaterial 3D printer ruled by the Rayleigh-Plateau Instability of a thread of a viscous fluid encased within an immiscible curing elastomer solution. This method allows spherical inclusions of a fluid to be placed periodically within an elastic matrix thereby creating a periodic elastic material creating tailored elastic bandgaps by changing a handful of control parameters. The procedure allows a very simple and fast development of mechanical metamaterial samples, with a large application range. To wit, we present a 4D mechanic metamaterials by using a ferrofluid as the inclusion's material, which can be actuated by a constant or time-dependent external magnetic field, allowing the tuning of both the dispersion relation of elastic waves as well as their amplification and damping.   

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This work demonstrates the existence of a novel class of localized elastic modes, namely bound modes in the continuum (BICs), in architected elastic beams. Current designs to achieve localized modes in periodic structures require bandgaps and suffer from energy leakage into the surrounding. BICs have the unique property that their mode amplitude goes to zero outside a compact region and they thus have zero leakage. In addition, their frequencies lie in pass bands and the designs thus do not require any bandgaps. Such mode shapes arise due to specific stringent conditions on the geometry of the structure. This work considers beams with an array of periodic masses. By adding carefully engineered defects, we derive a systematic procedure to achieve BICs in our considered structures in the context of Euler-Bernoulli beam theory. This procedure yields a family of BICs by varying the location and geometry of the defects. Our predictions are complemented with numerical simulation and experimental measurements that demonstrate the existence of BICs. Such wave confinement has potential application as filters in sensors and in elastic wave signal processing.   

Hyperbolic lattice waves, band theory and boundary modes of high dimensional representations of infinite hyperbolic lattice

Regular lattices in non-Euclidean space offer a new platform of exotic wave states due to both the non-abelian nature of their translation groups and the curvature of the embedding space. Waves in Euclidean lattices are governed by Bloch's theorem, which originates from one-dimensional representations of their abelian translation groups. In contrast, non-Euclidean lattices are beyond Bloch's theorem. In this talk, we propose a fundamental framework for characterizing wave states in non-Euclidean lattices, where we introduce a new formulation for compatibility and equilibrium matrices, derive a band theory for infinite hyperbolic lattices where waves carry high-dimensional irreducible representations of their non-abelian translation groups, and a representation-based method of finding boundary modes in hyperbolic lattices. These results shed light on the dispersion, response, and boundary modes of hyperbolic lattices, which are fundamentally distinct from those of conventional crystals.   

Topological mechanics of hyperbolic and spherical Maxwell lattices

Maxwell lattices, which are at the verge of mechanical instability, are analogs of topological insulators. In fact, they can host boundary-localized excitations that are topologically protected via a bulk-boundary correspondence.  In periodic Euclidean lattices, it is known that the boundary modes' location along the edge is determined by the unit cell's geometry in the bulk. Straight lines of bonds (fibers) can be polarized, i.e. floppy modes can accumulate at one fiber's endpoint while depleting at the other.  By considering homogeneous Maxwell lattices embedded in manifolds of constant positive and negative Gaussian curvature, we show that the lattice's intrinsic curvature provides an additional way to manipulate the localization of the boundary modes. We test this idea on hyperbolic and spherical versions of the Euclidean-space kagome lattice. Thanks to spatial curvature, rings of corner-sharing triangles can have an arbitrary number of edges. Euclidean straight fibers of bonds are replaced by diverging geodesics which can have both endpoints on the same boundary component. By polarizing the fibers, soft modes can be moved to selected regions along the boundary. We show that curvature can interplay with topological polarization leading to rich new phenomena.   

Stress control in non-ideal Maxwell lattices via geometry

Maxwell lattice, on the verge of mechanical instability, can demonstrate topologically polarized zero modes (ZMs) and state of self-stresses (SSSs) which lead to drastically different stiffnesses on opposite boundaries. It is known in idealized Maxwell lattice models that interfaces with localized SSSs can focus external stress and protect the bulk from fracturing. However, in non-ideal Maxwell lattices (i.e. additively manufactured) where thin ligaments with bending stiffness instead of free-hinges connect the rigid elements, stress accumulates at these ligaments in patterns not captured by the topological polarization. We computationally studied the effect of such bending stiffness in non-ideal Maxwell lattices in terms of stress distributions.  We find that, by tuning the unit cell geometry, the stress distribution in these non-ideal Maxwell lattices can be controlled such that the amount of stress accumulated at the ligaments is small while the topological stress localization is preserved in the Maxwell lattice.   

A gauge-like elastic theory for conformal metamaterials

We develop a framework to understand the mechanics of a metamaterial sheet that can undergo local, biaxial dilations and rotations with no energy cost (a conformal metamaterial). We construct an elastic theory for the buckling of the sheet in the Föppl–von Kármán limit,  valid for small deformations, by introducing an additional, scalar gauge-like field that couples to the internal metric of the sheet. The resulting elastic energy can describe how an ideal conformal metamaterial buckles out-of-plane. We then introduce additional terms that explicitly break the gauge symmetry and discuss possible generalizations to understand the mechanics of metamaterial sheets more broadly.   

A self-pumping mechanical analogue of Aubry-André-Harper model

We present a mechanical analogue of the Aubry-André-Harper (AAH) model where adiabatic pumping can be triggered by the signal in a non-reciprocal way. This structure consists of a one-dimensional lattice with a bulk zero energy mode which is parametrized by an angle. Depending on the value of this angle, this system supports finite frequency edge modes as a consequence of non-zero Chern numbers of the bulk bands. Interestingly, due to interaction between these finite frequency edge modes and the bulk zero mode, we find a "self-pumping effect" meaning that excitation from the end with the edge mode excites the bulk zero mode which in turn transports (pumps) the excitation from that side to the other side of the system, leading to non-reciprocity.   

Mechanics of Two-Phase Auxetic Chevron Mechanical Metamaterial

Auxetic materials has two major categories: one is cellular/foam like materials, which experience auxetic effect due to the rotation of ribs or shape-change of pores, the other class is multi-phase composites, which experience auxetic effect due to the deformation of soft phase and the kinematic deformation of hard phase. The first category experiences dramatic volume change upon external loads. While the second category experiences small deformation upon external loads. The first materials have been extensively explored; however, very little efforts have been made on the second materials. In this study, new two-phase auxetic mechanical metamaterial with chevron structures are designed. The new designs significantly expand the auxetic materials in the second category. FE models of this new family of materials are developed in ABAQUS, in which the design parameters can vary in very large ranges defined in Python script. Auxeticity in different material orientations is quantified both analytically and numerically. Design spaces with auxeticity are identified via more than one hundred FE simulations. To prove the concept, selected designs are fabricated via a multi-material 3D printer (Stratasys Connex3) and uni-axial tension tests are performed to measure the effective Poisson’s ratio and the stress-strain behavior.   

Probing nonequilibrium mechanical response of living chiral crystals

Developing starfish embryos can form living chiral crystals (LCC). Individual embryos swim, rotate, and interact non-reciprocally with each other. Broken time reversal symmetry leads to emergence of a variety of rich phenomena in this system, including chiral displacement waves. We investigate the interplay between nonequilibrium thermodynamics and mechanics, by applying frequency-dependent mechanical perturbations on LCCs. Interestingly, displacement waves can be excited by mechanical perturbation of LCC, and disturbed crystalline order can be restored. Our results can have potential implications for design and development of metamaterials.   

Poroelastic microlattices for underwater wave focusing

Architected materials consisting of open cell structures with microscale beam elements, i.e., microlattices, have demonstrated unprecedented quasi-static mechanical response and tailorable acoustic properties. When microlattices are coupled with pressure waves, the interplay between elastic waves in solid medium and pressure waves in surrounding fluid can be explained in the context of Biot theory. In this work, we characterize the acoustic properties of fluid-saturated elastic lattices under long wavelength approximation both numerically and experimentally. A Luneburg lens with modified index profile adapted for underwater wave focusing is demonstrated via the finite element analysis. We experimentally validate this design by 3D printing a gradient-index lens consisting of octet trusses with a spatially varying beam radius. Our method showcases a computationally efficient homogenization design approach that enables accelerated design of acoustic wave manipulation devices. By matching the acoustic impedance with surrounding fluid, microlattices with extraordinary stiffness-to-density ratio and enhanced transmission will prove useful for biomedical applications.