0000000000148154
AUTHOR
Mikko J. Alava
Crack dynamics and crack surfaces in elastic beam lattices
The dynamics of propagating cracks is analyzed in elastic two-dimensional lattices of beams. At early times, inertia effects and static stress enhancement combine so that the crack-tip velocity is found to behave as t1/7. At late times a minimal crack-tip model reproduces the numerical simulation results. With no disorder and for fast loading, a “mirror-mist-mirror” crack-surface pattern emerges. Introduction of disorder leads, however, to the formation of the “mirror-mist-hackle”–type interface typical in many experimental situations. Peer reviewed
Temporal and spatial persistence of combustion fronts in paper
The spatial and temporal persistence, or first-return distributions are measured for slow-combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on the front dynamics, which asymptotically belongs to the Kardar-Parisi-Zhang universality class. The stationary short-range and the transient behavior of the fronts are non-Markovian, and the observed persistence properties thus do not agree with the predictions based on Markovian theory. This deviation is a consequence of additional time and length scales, related to the crossovers to the asymptotic coarse-grained behavior. Peer reviewed
Kinetic Roughening in Slow Combustion of Paper
Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal development of the interface fluctuations. The asymptotic scaling properties, on long length and time scales, are well described by the Kardar-Parisi-Zhang (KPZ) equation with short-range, uncorrelated noise. To obtain a more detailed picture of the strong-coupling fixed point, characteristic of the KPZ universality class, universal amplitude ratios, and the universal coupling constant are computed from the data and found to be in good agreement with theory. Below …
Kardar–Parisi–Zhang scaling in kinetic roughening of fire fronts
Abstract We show that the roughening of fire fronts in slow combustion of paper [7] follows the scaling predictions of the Kardar–Parisi–Zhang equation with thermal noise. By improved experimental accuracy it is now possible to observe the short-time and short-range correlations of the interfaces. These do not adhere to any standard picture, and in particular, do not seem to be related to any of the existing models of front propagation in the presence of quenched disorder.
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
Permeability of three-dimensional random fiber webs
We report the results of essentially ab initio simulations of creeping flow through large threedimensional random fiber webs that closely resemble fibrous sheets such as paper and nonwoven fabrics. The computational scheme used in this Letter is that of the lattice-Boltzmann method and contains no free parameters concerning the properties of the porous medium or the dynamics of the flow. The computed permeability of the web is found to be in good agreement with experimental data, and confirms that permeability depends exponentially on porosity over a large range of porosity. [S0031-9007(97)05087-4]
Scaling and Noise in Slow Combustion of Paper
We present results of high resolution experiments on kinetic roughening of slow combustion fronts in paper, focusing on short length and time scales. Using three different grades of paper, we find that the combustion fronts show apparent spatial and temporal multiscaling at short scales. The scaling exponents decrease as a function of the order of the corresponding correlation functions. The noise affecting the fronts reveals short range temporal and spatial correlations, and non-Gaussian noise amplitudes. Our results imply that the overall behavior of slow combustion fronts cannot be explained by standard theories of kinetic roughening. Peer reviewed
Growth, percolation, and correlations in disordered fiber networks
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree of clustering. For $p=1$, the deposited network is uniformly random, while for $p=0$ only a single connected cluster can grow. For $p=0$, we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. For $p>0$, we carry out extensive simulations on fibers, and also needles and disks to study the dependence of the percolation threshold on $p$. We also derive a mean-field theory for the threshold ne…
Strength distribution in paper
Abstract Tensile strength distributions are studied in four paper samples that exhibit a variety of brittle-to-ductile properties. 1005 tensile specimens were measured in each case. The standard Gumbel and Weibull distributions, and a recently proposed double exponential modification of the former are compared with the observations visually and using chi-squared and Kolmogorov–Smirnov tests. The Gumbel distribution fails to fit the data while the Weibull distribution gives satisfactory agreement. However, the double exponential distribution fits the data best, regardless of the ductility of the material.
Roughening of a propagating planar crack front
A numerical model of the front of a planar crack propagating between two connected elastic plates is investigated. The plates are modeled as square lattices of elastic beams. The plates are connected by similar but breakable beams with a randomly varying stiffness. The crack is driven by pulling both plates at one end in Mode I at a constant rate. We find $\ensuremath{\zeta}=1/3, z=4/3,$ and $\ensuremath{\beta}=1/4$ for the roughness, dynamical, and growth exponents, respectively, that describe the front behavior. This is similar to continuum limit analyses based on a perturbative stress-intensity treatment of the front [H. Gao and J. R. Rice, J. Appl. Mech. 56, 828 (1989)]. We discuss the …