Topological defects produce exotic mechanics in complex metamaterials

Abstract

Defects, and in particular topological defects, are architectural motifs that play a crucial role in natural materials. Here we provide a systematic strategy to introduce such defects in mechanical metamaterials. We first present metamaterials that are a mechanical analogue of spin systems with tunable ferromagnetic and antiferromagnetic interactions, then design an exponential number of frustration-free metamaterials, and finally introduce topological defects by rotating a string of building blocks in these metamaterials. We uncover the distinct mechanical signature of topological defects by experiments and simulations, and leverage this to design complex metamaterials in which we can steer deformations and stresses towards parts of the system. Our work presents a new avenue to systematically include spatial complexity, frustration, and topology in mechanical metamaterials.arXiv:1903.07919v1 [cond-mat.soft]

Response evolution of mechanical metamaterials under architectural transformations

“…We now demonstrate the efficacy of predicting the stress response difference using SS-states-an approach valid for any mechanical network architecture-in a particular class of structurally complex mechanical metamaterials [19]. Their specific architecture allows us to easily enumerate and construct a basis of SS-space consisting of highly spatially localized states, and we show later that this complete description of SS-space produces a direct prediction of the stress response difference between two networks of differing designs under identical, external, supported loads.…”

“…Recently, we presented a systematic strategy to introduce defects, and in particular topological defects, in a novel class of mechanical metamaterials [19]. These consist of 2D triangular building blocks, and are a mechanical analogue of spin systems with tunable ferromagnetic and antiferromagnetic interactions, where the nature of the interaction is set by the orientation of the building blocks.…”

“…We subsequently introduced (topological) defects in our metamaterials by rotating one or more building blocks. These architectural transformations affect the mechanical response and allow us to direct the stress concentration in these structures [19]. Similarly, bond cutting strategies have recently been used to modify the elastic moduli of disordered networks [22][23][24], and spatial deformations in allosteric networks [25].…”

“…Here we extend this formalism to bond swapping, which involves the sequential cutting and adding of bonds. We focus on rotations of building blocks for a particular class of mechanical metamaterials [19], in which the resulting mechanical consequences are tractable.…”

“…We conclude that the stress response difference between networks with related architectures must be spanned by their mutually exclusive SS-states (section 2). We then present our non-periodic compatible mechanical metamaterials, consisting of stacked anisotropic building blocks that can deform in harmony [19] (section 3), and in which the SS-space can be represented as a set of localized states (section 4). We demonstrate how sequential building-block rotations produce architectural changes that introduce controlled frustration, producing varying configurations of (topological) defects (section 5).…”