Soft Mechanical Metamaterials with Transformable Topology Protected by Stress Caching.

Maxwell lattices possess distinct topological states that feature mechanically polarized edge behaviors and asymmetric dynamic responses protected by the topology of their phonon bands. Until now, demonstrations of non-trivial topological behaviors from Maxwell lattices have been limited to fixed configurations or have achieved reconfigurability using mechanical linkages. Here, a monolithic transformable topological mechanical metamaterial is introduced in the form of a generalized kagome lattice made from a shape memory polymer (SMP). It is capable of reversibly exploring topologically distinct phases of the non-trivial phase space via a kinematic strategy that converts sparse mechanical inputs at free edge pairs into a biaxial, global transformation that switches its topological state. All configurations are stable in the absence of confinement or a continuous mechanical input. Its topologically-protected, polarized mechanical edge stiffness is robust against broken hinges or conformational defects. More importantly, it shows that the phase transition of SMPs that modulate chain mobility, can effectively shield a dynamic metamaterial's topological response from its own kinematic stress history, referred to as "stress caching". This work provides a blueprint for monolithic transformable mechanical metamaterials with topological mechanical behavior that is robust against defects and disorder while circumventing their vulnerability to stored elastic energy, which will find applications in switchable acoustic diodes and tunable vibration dampers or isolators.

Dynamics of Self-Dual Kagome Metamaterials and the Emergence of Fragile Topology.

Recent years have seen the discovery of systems featuring fragile topological states. These states of matter lack certain protection attributes typically associated with topology and are therefore characterized by weaker signatures that make them elusive to observe. Moreover, they are typically confined to special symmetry classes and, in general, rarely studied in the context of phononic media. In this Letter, we theoretically predict the emergence of fragile topological bands in the spectrum of a twisted kagome elastic lattice with threefold rotational symmetry, in the so-called self-dual configuration. A necessary requirement is that the lattice is a structural metamaterial, in which the role of the hinges is played by elastic finite-thickness ligaments. The interplay between the edge modes appearing in the band gaps bounding the fragile topological states is also responsible for the emergence of corner modes at selected corners of a finite hexagonal domain, which qualifies the lattice as a second-order topological insulator. We demonstrate our findings through a series of experiments via 3D scanning laser doppler vibrometry conducted on a physical prototype. The selected configuration stands out for its remarkable geometric simplicity and ease of physical implementation in the panorama of dynamical systems exhibiting fragile topology.

Omnimodal topological polarization of bilayer networks: Analysis in the Maxwell limit and experiments on a 3D-printed prototype.

Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundaries. Topologically polarized Maxwell lattices, in particular, focus these zero modes to one of their boundaries in a manner that is protected against disorder by the reciprocal-space topology of the lattice's band structure. Here, we introduce a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane dilational and shearing modes to out-of-plane flexural modes, a paradigm that we refer to as "omnimodal polarization." While these structures exhibit a high-dimensional design space that makes it difficult to predict the topological polarization of generic geometries, we are able to identify a family of mirror-symmetric bilayers that inherit the in-plane modal localization of their constitutive monolayers, whose topological polarization can be determined analytically. Importantly, the coupling between the layers results in the emergence of omnimodal polarization, whereby in-plane and out-of-plane edge modes localize on the same edge. We demonstrate these theoretical results by fabricating a mirror-symmetric, topologically polarized kagome bilayer consisting of a network of elastic beams via additive manufacturing and confirm this finite-frequency polarization via finite element analysis and laser-vibrometry experiments.

Nonlinear harmonic generation in two-dimensional lattices of repulsive magnets.

In this work, we provide experimental evidence of nonlinear wave propagation in a triangular lattice of repulsive magnets supported by an elastic foundation of thin pillars, and we interpret all the individual features of the nonlinear wave field through the lens of a phonon band calculation that precisely accounts for the interparticle repulsive forces. We confirm the coexistence of two spectrally distinct components (homogeneous and forced) in the wave response that is induced via second harmonic generation (SHG) as a result of the quadratic nonlinearity embedded in the magnetic interaction. The detection of the forced component, specifically, allows us to attribute unequivocally the generation of harmonics to the nonlinear mechanisms germane to the lattice. We show that the spatial characteristics of the second harmonic components are markedly different from those exhibited by the fundamental harmonic. This endows the lattice with a functionality enrichment capability, whereby additional modal characteristics and directivity patterns can be triggered and tuned by merely increasing the amplitude of excitation.

Doubly nonlinear waveguides with self-switching functionality selection capabilities.

In this article, we investigate the effects of the interplay between quadratic and cubic nonlinearities on the propagation of elastic waves in periodic waveguides. Through this framework, we unveil an array of wave control strategies that are intrinsically available in the response of doubly nonlinear systems and we infer some basic design principles for tunable elastic metamaterials. The objective is to simultaneously account for two sources of nonlinearity that are responsible for distinct and complementary phenomena and whose effects are therefore typically discussed separately in the literature. Our study explicitly targets the intertwined effects that the two types of nonlinearity exert on each other, which modify the way in which their respective signatures are observed in the dynamic response. Through two illustrative examples we show how the dispersion correction caused by cubic nonlinearity can be used as an internal switch, or mode selector, capable of tuning on or off certain high-frequency response features that are generated through quadratic mechanisms. To this end, a multiple scale analysis is employed to obtain a full analytical solution for the nonlinear response that includes a complete description of the dual frequency-wave number dispersion correction shifts induced on all the branches, and elucidates the conditions necessary for the establishment of phase matching conditions.

Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies.

Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic, laser-assisted experimental characterization of topological kagome lattices, aimed at elucidating their in-plane phononic and topological characteristics. We specifically explore the continuum elasticity limit, which is established when the ideal hinges that appear in the theoretical models are replaced by ligaments capable of supporting bending deformation, as observed for instance in realistic physical lattices. We reveal how the zero-energy floppy edge modes predicted for ideal configurations morph into finite-frequency phonon modes that localize at the edges. By probing the lattices with carefully designed excitation signals, we are able to extract and characterize all the features of a complex, low-frequency acoustic regime in which bulk modes and topological edge modes overlap and entangle in response. The experiments provide unequivocal evidence of the existence of strong asymmetric wave transport regimes at finite frequencies.

Anomaly-sensitive dictionary learning for structural diagnostics from ultrasonic wavefields.

This paper proposes a strategy for the detection and triangulation of localized anomalies, such as defects, inclusions, or damage zones, in solid and structural media. The method revolves around the construction of sparse representations of the structure's ultrasonic wavefield response, which are obtained by learning instructive dictionaries that form a suitable basis for the response data. The resulting sparse coding problem is cast as a modified dictionary learning task with additional spatial sparsity constraints enforced on the atoms of the learned dictionaries, which provide them with the ability to unveil anomalous regions in the physical domain. The proposed methodology is model-agnostic, i.e., it forsakes the need for a physical model and requires virtually no a priori knowledge of the material properties. This characteristic makes the approach especially powerful for anomaly identification in systems with unknown or highly heterogeneous property distribution, for which a material model is unsuitable or unreliable. The method is tested against synthetically generated data as well as experimental data acquired using a scanning laser Doppler vibrometer.

Automated defect localization via low rank plus outlier modeling of propagating wavefield data.

This work proposes an agnostic inference strategy for material diagnostics, conceived within the context of laser-based nondestructive evaluation methods which extract information about structural anomalies from the analysis of acoustic wavefields measured on the structure's surface by means of a scanning laser interferometer. The proposed approach couples spatiotemporal windowing with low rank plus outlier modeling, to identify a priori unknown deviations in the propagating wavefields caused by material inhomogeneities or defects, using virtually no knowledge of the structural and material properties of the medium. This characteristic makes the approach particularly suitable for diagnostics scenarios in which the mechanical and material models are complex, unknown, or unreliable. We demonstrate our approach in a simulated environment using benchmark point and line defect localization problems based on propagating flexural waves in a thin plate.