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Multifunctional twisted kagome lattices: Tuning by pruning mechanical metamaterials.

Danilo B Liarte1, O Stenull2, T C Lubensky2

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This study explores elastic properties in diluted lattices, revealing jamming transitions where bulk and shear moduli change abruptly. These findings offer new ways to tune material properties for advanced metamaterials.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Mechanical Engineering

Background:

  • Randomly diluted lattices, like kagome and honeycomb structures, are crucial in materials science.
  • Understanding their elastic response, particularly bulk (B) and shear (G) moduli, is key to designing new materials.
  • Previous research has explored rigidity and jamming phenomena in various lattice structures.

Purpose of the Study:

  • To investigate the elastic properties and phonon behavior in novel lattices formed by combining twisted kagome with untwisted kagome or honeycomb lattices.
  • To analyze the critical endpoints and percolation transitions in these randomly diluted systems.
  • To explore the tunability of elastic moduli and the Poisson ratio through random dilution.

Main Methods:

  • Construction of composite lattices by adding next-nearest neighbor bonds between twisted kagome, untwisted kagome, and honeycomb lattices.
  • Analysis of elastic response and jamming phenomena through theoretical modeling and simulation.
  • Investigation of critical endpoints and rigidity percolation transitions.

Main Results:

  • Identified jamming-like critical endpoints where bulk modulus (B) and/or shear modulus (G) jump discontinuously from zero.
  • Observed lines of continuous rigidity percolation transitions where both B and G grow continuously from zero.
  • Demonstrated that the Poisson ratio and G/B can be continuously tuned via random dilution, similar to 'tuning by pruning'.

Conclusions:

  • The studied composite lattices exhibit unique jamming and percolation behaviors, offering precise control over elastic properties.
  • Random dilution provides a versatile method for tuning the mechanical response of these lattices.
  • These findings have implications for the design and fabrication of advanced metamaterials using techniques like 3D printing.