In recent years, mechanical metamaterials have been developed that support the propagation of an intriguing variety of nonlinear waves, including transition waves and vector solitons (solitons with coupling between multiple degrees of freedom). Here we report observations of phase transitions in 2D multistable mechanical metamaterials that are initiated by collisions of soliton-like pulses in the metamaterial. Analogous to first-order phase transitions in crystalline solids, we observe that the multistable metamaterials support phase transitions if the new phase meets or exceeds a critical nucleus size. If this criterion is met, the new phase subsequently propagates in the form of transition waves, converting the rest of the metamaterial to the new phase. More interestingly, we numerically show, using an experimentally validated model, that the critical nucleus can be formed via collisions of soliton-like pulses. Moreover, the rich direction-dependent behavior of the nonlinear pulses enables control of the location of nucleation and the spatio-temporal shape of the growing phase.

In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of elastic vector solitons, another type of nonlinear wave, in a multistable mechanical system with coupling between translational and rotational degrees of freedom. We experimentally observe the nucleation of a phase transformation arising from colliding waves, and we numerically investigate head-on and overtaking collisions of solitary waves with vectorial properties (i.e., elastic vector solitons). Unlike KdV-type solitons, which maintain their shape despite collisions, our system shows that collisions of two vector solitons can cause nucleation of a new phase via annihilation of the vector solitons, triggering the propagation of transition waves. The propagation of these depends both on the amount of energy carried by the vector solitons and on their respective rotational directions. The observation of the initiation of transition waves with collisions of vector solitons in multistable mechanical systems is an unexplored area of fundamental nonlinear wave interactions and could also prove useful in applications involving reconfigurable structures.

In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as an initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.

In this Letter, we introduce a paradigm to realize magnetomechanical metastructures inspired by multilayer two-dimensional materials, such as graphene bilayers. The metastructures are intended to capture two aspects of their nanoscale counterparts. One is the multilayer geometry, which is implemented by stacking hexagonal lattice sheets. The other is the landscape of weak interlayer forces, which is mimicked by the interactions between pairs of magnets located at corresponding lattice sites on adjacent layers. We illustrate the potential of this paradigm through a three-layer prototype. The two rigid outer lattices serve as control layers, while the thin inner layer is free to experience flexural motion under the confining action of the magnetic forces exchanged with the outer ones, thus behaving as a lattice on an elastic foundation. The inner layer is free to rotate relative to the others, giving rise to a rich spectrum of interlayer interaction patterns. Our objective is to determine how the dynamical response can be tuned by changing the twist angle between the layers. Specifically, we demonstrate experimentally that switching between different stacking patterns has profound consequences on the phonon landscape, opening and closing band gaps in different frequency regimes.

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.

In this work, we investigate the dynamics of interacting particle systems subjected to repulsive forces, such as lattices of magnetized particles. To this end, we first develop a general model capable of capturing the complete dynamical behavior of interacting particle systems governed by arbitrary potentials. The model elucidates the important role played by the static repulsive forces exchanged between particles in the initial equilibrium configuration, which is distilled and mathematically captured by a dedicated component of the stiffness matrix. The implications of the model are then examined through the simple illustrative example of a magnetic particle oscillator, by which we show that the effect associated with the initial static forces is germane to two- or higher-dimensional particle systems and vanishes for one-dimensional (1D) chains. In the context of wave propagation, we show that this type of effect manifests as modal-selective corrections of the dispersion relation of 2D repulsive lattices. To corroborate these findings, we perform laser vibrometry experiments on a lattice prototype consisting of a triangular grid of magnets supported by an elastic foundation of thin pillars. The tests unequivocally confirm the emergence of distinctive dispersive regimes in quantitative accordance to the model.