Edge-selective reconfiguration in polarized lattices with magnet-enabled bistability

Abstract

The signature topological feature of Maxwell lattices is their polarization, which manifests as an unbalance in stiffness between opposite edges of a finite domain. The manifestation of this asymmetry is especially dramatic in the case of soft lattices undergoing large nonlinear deformation under concentrated loads, where the excess of softness at the soft edge can result in the activation of sharp indentations. This study explores how this mechanical dichotomy between edges can be tuned and possibly extremized by working with soft magneto-mechanical metamaterials. The magneto-mechanical coupling is obtained by endowing the lattice sites with permanent magnets, which activate a network of magnetic forces that can interact with (either augmenting or competing with) the elasticity of the material. Specifically, under sufficiently large deformation that macroscopically alters the equilibrium positions of the sites, the attractive forces between the magnets can trigger bistable reconfiguration mechanisms. The strength of such mechanisms depends on the landscapes of elastic reaction forces exhibited by the edges, which are different due to the polarization, and is therefore inherently edge-selective. We show that, on the soft edge, the addition of magnets simply enhances the softness of the edge. In contrast, on the stiff edge, the magnets activate snapping mechanisms that locally reconfigure the cells and produce a lattice response reminiscent of plasticity, characterized by residual deformation that persists upon unloading.