Abstract
Competing ground states may lead to topologically constrained excitations such as domain walls or quasiparticles, which govern metastable states and their dynamics. Domain walls and more exotic topological excitations are well studied in magnetic systems such as artificial spin ice, in which nanoscale magnetic dipoles are placed on geometrically frustrated lattices, giving rise to highly degenerate ground states. We propose a mechanical spin-ice constructed from a lattice of floppy, bistable square unit cells. We compare the domain wall excitations that arise in this metamaterial to their magnetic counterparts, finding that new behaviors emerge in this overdamped mechanical system. By tuning the ratios of the internal elements of the unit cell, we control the curvature and propagation speed of internal domain walls. We change the domain wall morphology from a binary, strictly spin-like regime, to a more continuous, elastic regime. In the elastic regime, we inject, manipulate, and expel domain walls via textured forcing at the boundaries. The system exhibits dynamical hysteresis, and we find a first-order dynamical transition as a function of the driving frequency. We demonstrate a forcing protocol that produces multiple, topologically-distinct steady cycles, which are protected by the differences in their internal domain wall arrangements. These distinct steady cycles rapidly proliferate as the complexity of the applied forcing texture is increased, thus suggesting that such mechanical systems could serve as useful model systems to study multistability, glassiness, and memory in materials.
Highlights
Mechanical metamaterials are often created by compatible coupling of unit cells that exhibit a floppy mode, so as to produce a desired global deformation [1]
We have demonstrated that our mechanical analog of spin-ice exhibits real-space topological defects, to magnetic and other realizations of artificial spin ice (ASI)
These domain walls tend to escape to the system boundaries, but they can sometimes be immobilized depending on the ratios of spring stiffnesses used to construct the metamaterial or on imposed boundary conditions
Summary
Mechanical metamaterials are often created by compatible coupling of unit cells that exhibit a floppy mode, so as to produce a desired global deformation [1]. The mechanical floppy mode is such that the deformation of each unit-cell edge may be mapped to a binary spin within a ground-state ASI vertex. If the face nodes where the triangles meet are treated as pseudospins, this global mechanism maps to the ground states in magnetic ASI [Fig. 1(d)], for which each vertex has two opposing spins pointing inwards and two spins pointing outwards.
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