Transformable topological mechanical metamaterials

Abstract

Mechanical metamaterials are engineered materials whose structures give them novel mechanical properties, including negative Poisson's ratios, negative compressibilities and phononic bandgaps. Of particular interest are systems near the point of mechanical instability, which recently have been shown to distribute force and motion in robust ways determined by a nontrivial topological state. Here we discuss the classification of and propose a design principle for mechanical metamaterials that can be easily and reversibly transformed between states with dramatically different mechanical and acoustic properties via a soft strain. Remarkably, despite the low energetic cost of this transition, quantities such as the edge stiffness and speed of sound can change by orders of magnitude. We show that the existence and form of a soft deformation directly determines floppy edge modes and phonon dispersion. Finally, we generalize the soft strain to generate domain structures that allow further tuning of the material.

Sonic Landau Levels and Synthetic Gauge Fields in Mechanical Metamaterials

“…We show how this domain-wall-bound mode exhibits robustness against a type of disorder that may come in the manufacturing of acoustic metamaterialsdisorder in the stiffness of each component. Like other realizations of topological states [15,16] in mechanical [17][18][19][20][21][22][23][24][25][26][27], acoustic [28][29][30][31][32][33][34][35][36], and photonic [37] metamaterials, this characterization may help with the design of robust devices. We show that introducing dissipation on just one of the two sublattices enhances the domain-wall-bound sound mode.…”

Topological Edge Floppy Modes in Disordered Fiber Networks

“…A simple two-dimensional example of Maxwell lattice, the deformed kagome lattice, as shown in Fig. 1, exhibit different phases where the topological structure changes and the floppy modes localize at different edges [17]. In particular, what drives the topological transition here is a soft strain that changes the lattice geometry, where all bonds remain the same length and only the bond angles alter.…”

“…In the topologically nontrivial phase all floppy modes localize on the top edge leaving the bottom edge rigid. This physics of the Maxwell lattices make them both an interesting topic for theoretical study [21][22][23][24][25][26][27] and good candidates for the design of novel mechanical metamaterials where the edges can change stiffness by orders of magnitude reversibly [17].…”

“…Among many different types of topological mechanical systems, a particularly interesting class consists of "Maxwell lattices", which are central-force lattices with average coordination number z = 2d where d is the spatial dimension, and are thus at the verge of mechanical instability [2,3,[16][17][18][19][20]. Maxwell lattices host topologically protected phonon edge modes at zero frequency (floppy modes).…”

“…Introduction -Recent theoretical advances in applying concepts of topological states of matter to mechanical systems has led to the burgeoning new field of "topological mechanics", where nontrivial topologies of the phonon bands give rise to exotic mechanical and acoustic properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”