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Rigidity transition in two-dimensional random fiber networks.

M Latva-Kokko1, J Mäkinen, J Timonen

  • 1Department of Physics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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Rigidity percolation in 2D fibrous networks was studied using two methods to add constraints. Both methods lead to a rigid network at critical probabilities, falling into the same universality class.

Area of Science:

  • Physics
  • Materials Science
  • Network Theory

Background:

  • Rigidity percolation is crucial for understanding the mechanical properties of disordered materials.
  • Fibrous networks are ubiquitous in nature and engineering, exhibiting complex mechanical behaviors.

Purpose of the Study:

  • To analyze rigidity percolation in two-dimensional (2D) random fibrous networks.
  • To investigate two novel strategies for introducing rigidity into these networks.

Main Methods:

  • Modeling fibrous networks with central forces between adjacent fiber crossing points.
  • Incorporating rigidity by adding constraints between second-nearest crossing points with probability p(sn).
  • Introducing rigidity by "welding" crossing points, fixing fiber angles with probability p(weld).

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Main Results:

  • Identified critical probabilities p(sn)(c) and p(weld)(c) at which the networks become rigid.
  • Provided accurate estimates for transition thresholds and associated critical exponents.
  • Demonstrated that both rigidity strategies belong to the same universality class.

Conclusions:

  • The two introduced strategies effectively induce rigidity in 2D fibrous networks.
  • The rigidity transition in these models aligns with that of 2D central-force rigidity percolation in diluted lattices.
  • Findings contribute to the understanding of mechanical properties in disordered network materials.