  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.
