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The effective transport properties of heterogeneous nanoscale materials and structures are affected by several geometrical and physical factors. Among them the presence of imperfect interfaces plays a central role being often at the origin…

Metamaterials are constructed such that, for a narrow range of frequencies, the momentum density depends on the local displacement gradient, and the stress depends on the local velocity. In these models the momentum density generally…

Mechanical extremal materials, a class of metamaterials that exist at the bounds of elastic theory, possess the extraordinary capability to engineer any desired elastic behavior by harnessing mechanical zero modes -- deformation modes that…

There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the…

Multi-step pathways, constituted of a sequence of reconfigurations, are central to a wide variety of natural and man-made systems. Such pathways autonomously execute in self-guided processes such as protein folding and self-assembly, but…

For most acoustic metamaterials, once they have been fabricated, their operating frequencies and functions cannot be adjusted, which is an intrinsic barrier for development of realistic applications. The study to overcome this limit has…

Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…

Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…

Artificial Spin Ices are two dimensional arrays of magnetic, interacting nano-structures whose geometry can be chosen at will, and whose elementary degrees of freedom can be characterized directly. They were introduced at first to study…

The transformation method is a powerful tool for providing the constitutive parameters of the transformed material in the new coordinates. In transformation elasticity, a general curvilinear change of coordinates transforms conventional…

Mechanical metamaterials composed of bistable elements have recently emerged as promising platforms for mechanical memory. Traditional approaches to writing information in these systems typically rely on localized actuation or predefined…

Mechanical metamaterials are artifical composites that exhibit a wide range of advanced functionalities such as negative Poisson's ratio, shape-shifting, topological protection, multistability, and enhanced energy dissipation. To date, most…

Topological metamaterials unlock confined and robust elastic wave control in mechanical structures. Recent breakthroughs have precipitated the development of 3D topological mechanical metamaterials, which extend beyond the conventional 1D…

Recently, a class of mechanical lattices with reconfigurable, zero-stiffness structures has been proposed, called Totimorphic lattices. In this work, we introduce a computational framework that enables continuous reprogramming of a…

The subject of mechanical metamaterials has been gaining significant attention, however, their widespread application is still halted. Such materials are usually considered as stand-alone, vis-\`a-vis all characteristic length scales being…

In the past two decades, artificial structures known as metamaterials have been found to exhibit extraordinary material properties that enable the unprecedented manipulation of electromagnetic waves, elastic waves, molecules, and particles.…

Tunable metasurfaces enable active and on-demand control over optical wavefronts through reconfigurable scattering of resonant nanostructures. Here, we present novel insights inspired by mechanical metamaterials to achieve giant tunability…

Granular media near jamming exhibit fascinating properties, which can be harnessed to create jammed-granulate metamaterials: materials whose characteristics arise not only from the shape and material properties of the particles at the…

The conventional description of time-varying media assumes that electromagnetic fields evolve according to fixed continuity conditions during parameter jumps. Here we reveal that these conditions are not physical constraints but tunable…

Waves impart momentum and exert force on obstacles in their path. The transfer of wave momentum is a fundamental mechanism for contactless manipulation, yet the rules of conventional scattering intrinsically limit the radiation force based…