Viscoelastic scaling regimes for marginally-rigid fractal spring networks

Abstract

A family of marginally-rigid (isostatic) spring networks with fractal structure up to a controllable length was devised and the viscoelastic spectra $G^{\ast }(\omega )$ calculated. Two non-trivial scaling regimes were observed, (i)~$G^{\prime }\approx G^{\prime \prime }\propto {\omega }^{\Delta }$ at low frequencies, consistent with $\Delta =1/2$; (ii)~$G^{\prime }\propto G^{\prime \prime }\propto {\omega }^{{\Delta }^{\prime }}$ for intermediate frequencies corresponding to fractal structure, consistent with a theoretical prediction ${\Delta }^{\prime }=(\ln 3-\ln 2)/(\ln 3+\ln 2)$. The cross-over between these two regimes occurred at lower frequencies for larger fractals in a manner suggesting diffusive-like dispersion. Solid gels generated by introducing internal stresses exhibited similar behaviour above a low-frequency cut-off, indicating the relevance of these findings to real-world applications.

arXiv comment5 pages, 3 figures. Expanded text and 3 new SI figures. To appear in PRL

References in corpus (21)

• Effects of compression on the vibrational modes of marginally jammed solids
• Ageing and Rheology in Soft Materials
• A coordination-based approach to elasticity of floppy and stiff random networks
• Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
• Cross-link governed dynamics of biopolymer networks
• Diffusion- and reaction-limited cluster aggregation revisited
• A minimal-length approach unifies rigidity in under-constrained materials
• Normal Modes in Model Jammed Systems in Three Dimensions
• Power law viscoelasticity of a fractal colloidal gel
• The Glassy Wormlike Chain
• Origin of slow stress relaxation in the cytoskeleton
• Elasticity of Filamentous Kagome Lattice
• Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids
• Geometry and the onset of rigidity in a disordered network
• Floppiness, cutting, and freezing: Dynamic critical scaling near isostaticity
• Dynamical behavior of disordered spring networks
• Structural hierarchy confers error tolerance in biological tissues
• Microrheological approach for the viscoelastic response of gels
• Non-affinity and fluid-coupled viscoelastic plateau for immersed fiber networks
• Correlated rigidity percolation in fractal lattices
• Self-stresses control stiffness and stability in overconstrained disordered networks