Nonreciprocal elasticity and the realization of static and dynamic nonreciprocity

Abstract

The realization of the mechanical nonreciprocity requires breaking either the time-reversal symmetry or the material deformation symmetry. The time-reversal asymmetry was the commonly adopted approach to realize dynamic nonreciprocity. However, a static nonreciprocity requires—with no any other option—breaking the material deformation symmetry. By virtue of the Maxwell–Betti reciprocal theorem, the achievement of the static nonreciprocity seems to be conditional by the use of a nonlinear material. Here, we further investigate this and demonstrate a novel “nonreciprocal elasticity” concept. We investigated the conditions of the attainment of effective static nonreciprocity. We revealed that the realization of static nonreciprocity requires breaking the material deformation symmetry under the same kinematical and kinetical conditions, which can be achieved only and only if the material exhibits a nonreciprocal elasticity. By means of experimental and topological mechanics, we demonstrate that the realization of static nonreciprocity requires nonreciprocal elasticity no matter what the material is linear or nonlinear. We experimentally demonstrated linear and nonlinear metamaterials with nonreciprocal elasticities. The developed metamaterials were used to demonstrate that nonreciprocal elasticity is essential to realize static nonreciprocal-topological systems. The nonreciprocal elasticity developed here will open new venues of the design of metamaterials that can effectively break the material deformation symmetry and achieve, both, static and dynamic nonreciprocity.

Mechanical nonreciprocity in a uniform composite material

“…One simple example is the realization of nonreciprocal transmission of the displacement field through the fabrication of silicon rubber into a fishbone-structured metamaterial ( 10 ). However, mechanical nonreciprocity has so far mainly been realized through the complicated design of active robotics ( 15 , 16 ) or metamaterial frameworks ( 17 , 18 ). Even the most advanced systems still rely on the shaping and connection of reciprocal materials, which limits the design freedom and practical applications of such systems.…”

Programmable nonreciprocal Poynting effect enabled by lattice metamaterials

“…Recently, there has been a growing interest in breaking the symmetry of signal transmission in both temporal and spatial dimensions to induce nonreciprocal behaviors, mainly in dynamic systems involving electromagnetic (3)(4)(5), acoustic (6)(7)(8), and mechanical (9-13) wave propagation. Static nonreciprocity introduces a unique ability to manipulate mechanical signals and energy without requiring active time-modulated components (14)(15)(16)(17)(18). For example, Coulais et al (14) broke the Maxwell-Betti reciprocity theorem with a fishbone metamaterial, revealing static shear nonreciprocity.…”

Spectral entropy and strain energy trends in composite mechanical metamaterials

“…The macroscopic response of the metamaterial is assessed based on an effective medium description without explicitly taking into account internal degrees of freedom, inhomogeneities or other components that exist within the structure. A wide range of mechanical behavior is realized across the different architectures for example, negative effective elastic constants [4][5][6][7], multistable structures [8][9][10][11][12][13][14], reversal of Saint Venant end effects [10], static non-reciprocity [15,16] and other behaviors [17,18].…”