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This paper addresses fundamental questions arising in the theory of Bloch-Floquet waves in chiral elastic lattice systems. This area has received a significant attention in the context of "topologically protected" waveforms. Although…

We demonstrate a new method of achieving topologically protected states in a discrete hexagonal lattice by attaching gyroscopic spinners, which bring chirality to the system. Dispersive features of this medium are investigated in detail…

Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic…

The need for structuring on micrometer scales is abundant, for example, in view of phononic applications. We here outline a novel approach based on the phenomenon of active turbulence on the mesoscale. As we demonstrate, a shear-thickening…

Rotationally resonant metamaterials are leveraged to answer a longstanding question regarding the existence of transformation-invariant elastic materials and the ad-hoc possibility of transformationbased passive cloaking in full plane…

We develop a new asymptotic model of the dynamic interaction between an elastic structure and a system of gyroscopic spinners that make the overall multi-structure chiral. An important result is the derivation and analysis of effective…

In this paper, a coherent boundary value problem to model metamaterials' behavior based on the relaxed micromorphic model is established. This boundary value problem includes well-posed boundary conditions, thus disclosing the possibility…

Exploring the dynamical response of mechanical metamaterials has gathered increasing attention in the last decades, enabling the design of microstructures exotically interacting with elastic waves (focusing, channeling, band-gaps, negative…

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are…

Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…

We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…

Vortices are localized planar structures that attain topological stability and can be used to describe collective behavior in a diversity of situations of current interest in nonlinear science. In high energy physics, vortices engender…

In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…

Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…

Metamaterials enable the emergence of novel physical properties due to the existence of an underlying sub-wavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern…

The complex interactions of localized vortices with waves is investigated using a model of point vortices in the presence of a transverse or longitudinal wave. This simple model shows a rich dynamical behavior including oscillations of a…

Unlike conventional two-dimensional (2D) semiconductor superlattices, moir\'{e} patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a…

This article present the double-periodical lattice made of infinite elastic fibers that withstand bending and tension. The model describes the elastic properties of flat periodic structure. With this model the behavior of a two-dimensional…

Precise control of the polarization and propagation direction of elastic waves is a fundamental challenge in elastodynamics. Achieving efficient mode conversion along arbitrary paths with conventional techniques has proven difficult. In…