Correlated rigidity percolation in fractal lattices
arXiv:2008.12421 · doi:10.1103/PhysRevE.103.012104
Abstract
Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network. Specifically, we calculate the critical packing fractions of site-diluted lattices of Sierpiński gaskets (SG's) with varying degrees of fractal iteration. Our results suggest that although the correlation length exponent and fractal dimension of the RP of these lattices are identical to that of the regular triangular lattice, the critical volume fraction is dramatically lower due to the fractal nature of the network. Furthermore, we develop a simplified model for an SG lattice based on the fragility analysis of a single SG. This simplified model provides an upper bound for the critical packing fractions of the full fractal lattice, and this upper bound is strictly obeyed by the disorder averaged RP threshold of the fractal lattices. Our results characterize rigidity in ultra-low-density fractal networks.
arXiv comment7 pages, 8 figures
References in corpus (10)
- Jamming, Force Chains and Fragile Matter
- Gelation as condensation frustrated by hydrodynamics and mechanical isostaticity
- Algorithms for 3D rigidity analysis and a first order percolation transition
- Fracturing of topological Maxwell lattices
- Self-assembly and cooperative dynamics of a model colloidal gel network
- Emergence of Multiscale Dynamics in Colloidal Gels
- Fiber networks below the isostatic point: fracture without stress concentration
- Rigidity percolation on the square lattice
- Rigidity percolation by next-nearest-neighbor braces on generic and regular isostatic lattices
- Structural hierarchy confers error tolerance in biological tissues