( 2017).Īmong these fascinating systems right at the verge of mechanical instability, a subcategory, known as Maxwell networks/lattices Lubensky et al. By controlling these floppy modes, which are the low energy excitations of the system, mechanical response of a material can be precisely programmed, which has broad applications such as switchable, actuatable, deployable materials Bertoldi et al. One peculiar feature of these materials is that they can exhibit a small number of floppy modes, i.e., normal modes of deformation that cost little elastic energy, but at the same time remain stable under other types of loads. ( 2017) and topological states Kane and Lubensky ( 2014) Lubensky et al. ( 2010) Ellenbroek and Mao ( 2011) Ellenbroek et al.
At the verge between these two types of behaviors, interesting physics arises, such as critical phenomena Jacobs and Thorpe ( 1995) Liu et al. Mechanical stability is concerned with the response of a material to external loads-whether it holds its shape like a solid or flows like a liquid. The second type, which arise in thin plates with a small bending stiffness and a negative Gaussian curvature, exhibit fractional excitations and topological degeneracy, in strong analogy to Z 2 spin liquids and dimerized spin chains. The first type, which we name “Maxwell plates”, are in strong analogy with Maxwell lattices, and exhibit a sub-extensive number of holographic floppy modes.
In this paper we examine continuous elastic media on the verge of mechanical instability, extend Maxwell-Calladine index theorem to continua in the nonlinear regime, classify elastic media based on whether stress can be fully released,Īnd identify two types of elastic media with topological states. In contrast, topological states in continuum elasticity without repeating unit cells remain largely unexplored, but offer wonderful opportunities for both new theories and broad applications in technologies, due to their great convenience of fabrication.
In the past a few years, topologically protected mechanical phenomena have been extensively studied in discrete lattices and networks, leading to a rich set of discoveries such as topological boundary/interface floppy modes and states of self stress, as well as one-way edge acoustic waves.
0 kommentar(er)
