Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration

Abstract

Mechanical metamaterials present a promising platform for seemingly impossible mechanics. They often require incompatibility of their elementary building blocks, yet a comprehensive understanding of its role remains elusive. Relying on an analogy to ferromagnetic and antiferromagnetic binary spin interactions, we present a general approach to identify and analyze topological mechanical defects for arbitrary building blocks. We underline differences between two- and three-dimensional metamaterials, and show how topological defects can steer stresses and strains in a controlled and non-trivial manner and can inspire the design of materials with hitherto unknown complex mechanical response.

Kagome qubit ice

“…Among spin ices, the kagome ice model [10][11][12][13][14][15][16][17][18] has been widely studied because it mimics a remarkable variety of natural and artificial systems, from rare-earth pyrochlores [3], to nanomagnetic fabrications [19], gravitationally trapped colloids [15], and many other systems [20][21][22][23][24][25][26][27][28]. Kagome spin ice can in principle manifest various unusual phases [13][14][15], but the large energy scales of artificial implementations pose an experimental challenge; thorough measurements of these phases and the physical conditions driving the phase-to-phase transition are scarce.…”

Training precise stress patterns

“…In this paper, we introduce a training rule aimed at manipulating the stresses in an elastic network. 14,15 We consider a disordered network that is able to evolve through changes to the rest lengths. Each bond is taken to be a spring and dashpot in series, whose length changes in proportion to the tension on that bond.…”

Kagome qubit ice

“…Among spin ices, the kagome ice model [10][11][12][13][14][15][16][17][18] has been widely studied because it mimics a remarkable variety of natural and artificial systems, from rare-earth pyrochlores 3 , to nanomagnetic fabrications 19 , gravitationally trapped colloids 15 , as well as many others [20][21][22][23][24][25][26][27][28] . Kagome spin ice can in principle manifest unusual phases [13][14][15] , but the large energy scales of artificial implementations pose an experimental challenge; thorough measurements of these phases and the physical conditions driving the phase-to-phase transition are scarce, and an experimental description of their kinetics is entirely lacking.…”