0000000000613834
AUTHOR
M. Latva-kokko
The role of connectivity in the properties of sedimented materials
Effective-medium theories for both random packings of elastic discs and mats of randomly sedimented elastic fibers can be constructed such that the effective material stiffness depends on the stiffness and geometry of the constituents of the material, and the number density of contacts. It is demonstrated that the number density of contacts together with the geometry of the constituents also determine the porosity of these materials. The simplicity and similar structure of the effective-medium estimates for the properties of these two qualitatively different materials indicate that the number density of contacts may play a similar role in an appropriate effective-medium description of a lar…
Dynamic rigidity transition.
An inflated closed loop (or membrane) is used to demonstrate a dynamic rigidity transition that occurs when impact energy is added to the loop in static equilibrium at zero temperature. The only relevant parameter in this transition is the ratio of the energy needed to collapse the loop and the impact energy. When this ratio is below a threshold value close to unity, the loop collapses into a high-entropy floppy state, and it does not return to the rigid state unless the impact energy can escape. The internal oscillations are in the floppy state dominated by 1/f(2) noise. When the ratio is above the threshold, the loop does not collapse, and the internal oscillations resulting from the impa…
Rigidity transition in two-dimensional random fiber networks
Rigidity percolation is analyzed in two-dimensional random fibrous networks. The model consists of central forces between the adjacent crossing points of the fibers. Two strategies are used to incorporate rigidity: adding extra constraints between second-nearest crossing points with a probability p(sn), and "welding" individual crossing points by adding there four additional constraints with a probability p(weld), and thus fixing the angles between the fibers. These additional constraints will make the model rigid at a critical probability p(sn)=p(sn)(c) and p(weld)=p(weld)(c), respectively. Accurate estimates are given for the transition thresholds and for some of the associated critical e…
Rigidity of random networks of stiff fibers in the low-density limit.
Rigidity percolation is analyzed in two-dimensional random networks of stiff fibers. As fibers are randomly added to the system there exists a density threshold ${q=q}_{\mathrm{min}}$ above which a rigid stress-bearing percolation cluster appears. This threshold is found to be above the connectivity percolation threshold ${q=q}_{c}$ such that ${q}_{\mathrm{min}}=(1.1698\ifmmode\pm\else\textpm\fi{}{0.0004)q}_{c}.$ The transition is found to be continuous, and in the universality class of the two-dimensional central-force rigidity percolation on lattices. At percolation threshold the rigid backbone of the percolating cluster was found to break into rigid clusters, whose number diverges in the…
Clustering and viscosity in a shear flow of a particulate suspension
A shear flow of particulate suspension is analyzed for the qualitative effect of particle clustering on viscosity using a simple kinetic clustering model and direct numerical simulations. The clusters formed in a Couette flow can be divided into rotating chainlike clusters and layers of particles at the channel walls. The size distribution of the rotating clusters is scale invariant in the small-cluster regime and decreases rapidly above a characteristic length scale that diverges at a jamming transition. The behavior of the suspension can qualitatively be divided into three regimes. For particle Reynolds number Re(p) less than or approximately equal 0.1, viscosity is controlled by the char…