Multifunctional twisted kagome lattices: Tuning by pruning mechanical metamaterials

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.