Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial

Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are generally hyperstatic (or overconstrained). Here, we show how symmetries may be applied to generate topological soft modes even in overconstrained, rigid systems. To do so, we consider non-Hermitian topology based on non-square matrices, an...

Maxwell lattice metamaterials possess a rich phase space with distinct topological states featuring mechanically polarized edge behaviors and strongly asymmetric acoustic responses. Until now, demonstrations of non-trivial topological behaviors from Maxwell lattices have been limited to either monoliths with locked configurations or reconfigurable mechanical linkages. This work introduces a transformable topological mechanical metamaterial (TTMM) made from a shape memory poly...

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are often prohibitively expensive at scales of interest. Prior studies have therefore utilized low-order effective medium models, such as discrete mass-spring lattices, to capture essential properties in the long-wavelength limit. While models ...

Reciprocity is a fundamental principle governing various physical systems, which ensures that the transfer function between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity have been mostly considered in dynamic systems, for electromagnetic, acoustic and mechanical wave propagation as...

The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework successfully captures the physics of small systems under idealized conditions, large systems or heterogeneous driving conditions remain essentially unexplored. Here we uncover strong anomalies in the mechanics of a broad class of metamateria...

Mechanical metamaterials are those structures designed to convey force and motion in novel and desirable ways. Recently, Kane and Lubensky showed that lattices at the point of marginal mechanical stability (Maxwell lattices) possess a topological invariant that describes the distribution of floppy, zero-energy edge modes. Here, we show that applying force at a point in the bulk of these lattices generates a directional mechanical response, in which stress or strain is induced...

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic materials, geometric nonlinearity at finite strain, and a quasi-static response. The optimization problem is solved by a nonlinear programming method and the sensitivities computed via the adjoint method. Two-dimensional structures identifi...

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 s...

We present fracturing analysis of topological Maxwell lattices when they are stretched by applied stress. Maxwell lattices are mechanical structures containing equal numbers of degrees of freedom and constraints in the bulk and are thus on the verge of mechanical instability. Recent progress in topological mechanics led to the discovery of topologically protected floppy modes and states of self stress at edges and domain walls of Maxwell lattices. When normal brittle material...

Topological mechanical structures exhibit robust properties protected by topological invariants. In this letter, we study a family of deformed square lattices that display topologically protected zero-energy bulk modes analogous to the massless fermion modes of Weyl semimetals. Our findings apply to sufficiently complex lattices satisfying the Maxwell criterion of equal numbers of constraints and degrees of freedom. We demonstrate that such systems exhibit pairs of oppositely...