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Percolation transition in entangled granular networks.

Seongmin Kim1, Daihui Wu1, Yilong Han2,3

  • 1Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China.

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Network science reveals how C-shaped granular particles form solid-like structures through entanglement. A percolation transition occurs, forming a giant cluster above a critical link threshold, influenced by particle shape.

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Area of Science:

  • Physics of granular materials
  • Network science applications
  • Materials science

Background:

  • Nonconvex granular particles, like staples, form cohesive structures via geometric entanglement.
  • The network structure of these entangled materials is not well understood.

Purpose of the Study:

  • To investigate the entanglement networks of C-shaped granular particles using network science.
  • To analyze the formation and properties of these networks under vibration.

Main Methods:

  • Experimental studies of C-shaped granular particles under vibration.
  • Simulations to model particle entanglement.
  • Network analysis of key properties, including percolation transitions.

Main Results:

  • Entanglement networks exhibit a percolation transition as the number of links increases logarithmically.
  • A giant cluster forms when the number of links surpasses a critical threshold.
  • A continuum percolation model of rings effectively describes the observed transition.
  • The particles' opening angle significantly influences mechanical bonding and network structure.

Conclusions:

  • Network science provides a powerful framework for studying entangled granular materials.
  • The findings have implications for designing mechanical metamaterials and understanding complex entangled systems.
  • Particle geometry, specifically the opening angle, is crucial for network formation and mechanical properties.