Multi-functional Twisted-Kagome lattices: Tuning by Pruning Mechanical Metamaterials

Abstract

This article investigates phonons and elastic response in randomly diluted lattices constructed by combining (via the addition of next-nearest bonds) a twisted kagome lattice, with bulk modulus $B=0$ and shear modulus $G>0$, with either a generalized untwisted kagome lattice with $B>0$ and $G>0$ or with a honeycomb lattice with $B>0$ and $G=0$. These lattices exhibit jamming-like critical end-points at which $B$, $G$, or both $B$ and $G$ jump discontinuously from zero while the remaining moduli (if any) begin to grow continuously from zero. Pairs of these jamming points are joined by lines of continuous rigidity percolation transitions at which both $B$ and $G$ begin to grow continuously from zero. The Poisson ratio and $G/B$ can be continuously tuned throughout their physical range via random dilution in a manner analogous to "tuning by pruning" in random jammed lattices. These lattices can be produced with modern techniques, such as 3D printing, for constructing metamaterials.

11 pages, 10 figures

References in corpus (7)

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• Auxetic metamaterials from disordered networks
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• Dualities and non-Abelian mechanics
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Cited by in corpus (5)

• Elastostatics of star-polygon tile-based architectured planar lattices
• Jamming and Unusual Charge Density Fluctuations of Strange Metals
• Universal scaling for disordered viscoelastic matter near the onset of rigidity
• Control of connectivity and rigidity in prismatic assemblies
• Transformable Super-Isostatic Crystals Self-Assembled from Segment Colloidal Rods