0000000000613835
AUTHOR
J. P. Mäkinen
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…
Elasticity of Poissonian fiber networks
An effective-medium model is introduced for the elasticity of two-dimensional random fiber networks. These networks are commonly used as basic models of heterogeneous fibrous structures such as paper. Using the exact Poissonian statistics to describe the microscopic geometry of the network, the tensile modulus can be expressed by a single-parameter function. This parameter depends on the network density and fiber dimensions, which relate the macroscopic modulus to the relative importance of axial and bending deformations of the fibers. The model agrees well with simulation results and experimental findings. We also discuss the possible generalizations of the model. Peer reviewed
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…