Kinetics of multidimensional fragmentation (original) (raw)

Universal Dynamic Fragmentation in D Dimensions

Physical Review Letters, 2004

A generic model is introduced for brittle fragmentation in D dimensions, and this model is shown to lead to a fragment-size distribution with two distinct components. In the small fragment-size limit a scale-invariant size distribution results from a crack branching-merging process. At larger sizes the distribution becomes exponential as a result of a Poisson process, which introduces a large-scale cutoff. Numerical simulations are used to demonstrate the validity of the distribution for D 2. Data from laboratory-scale experiments and large-scale quarry blastings of granitic gneiss confirm its validity for D 3. In the experiments the nonzero grain size of rock causes deviation from the ideal model distribution in the small-size limit. The size of the cutoff seems to diverge at the minimum energy sufficient for fragmentation to occur, but the scaling exponent is not universal.

Dynamical scaling in fragmentation

Journal of Applied Physics, 1993

The dynamics of a fragmentation model is examined from the point of view of numerical simulation and rate equations. The model includes effects of temperature. The number n (s,t) of fragments of size s at time t is obtained and is found to obey the scaling form n(s,t)-s-rP'Ye-Pff(s/tZ) where f(x) is a crossover function satisfying f(x) N 1 for x< 1 and f(x) gl for x) 1. The dependence of the critical exponents 7; w, 7, and z on space dimensionality d is studied from d= 1 to 5. The result of the dynamics on fractal and nonfractal objects as well as on square and triangular lattices is also examined.

Schematic models for fragmentation of brittle solids in one and two dimensions

Physica A: Statistical …, 2007

Stochastic models for the development of cracks in 1 and 2 dimensional objects are presented. In one dimension, we focus on particular scenarios for interacting and non-interacting fragments during the breakup process. For two dimensional objects, we consider only non-interacting fragments, but analyze isotropic and anisotropic development of fissures. Analytical results are given for many observables. Power-law size distributions are predicted for some of the fragmentation pictures considered.

Dimensional effects in dynamic fragmentation of brittle materials

Physical Review E, 2005

It has been shown previously that dynamic fragmentation of brittle D-dimensional objects in a D-dimensional space gives rise to a power-law contribution to the fragment-size distribution with a universal scaling exponent 2−1/D. We demonstrate that in fragmentation of two-dimensional brittle objects in threedimensional space, an additional fragmentation mechanism appears, which causes scale-invariant secondary breaking of existing fragments. Due to this mechanism, the power law in the fragment-size distribution has now a scaling exponent of ϳ1.17.

Large-Scale Simulations of a Bi-dimensional n-Ary Fragmentation Model

Lecture Notes in Computer Science, 2006

A bi-dimensional n-ary fragmentation model is numerically studied by large-scale simulations. Its main assumptions are the existence of random point flaws and a fracture mechanism based on the larger net force. For the 4-ary fragment size distribution it was obtained a power law with exponent 1.0 ≤ β ≤ 1.15 . The visualizations of the model resemble brittle material fragmentation.

Scaling laws in fragmentation kinetics

Physica A: Statistical Mechanics and its Applications

We investigate disruptive collisions of aggregates comprised of particles with different interaction potentials. We study Lennard-Jones (L-J), Tersoff, modified L-J potential and the one associated with Johnson-Kendall-Roberts (JKR) model. These refer to short, middle and long-ranged inter-particle potentials and describe both inter-atomic interactions and interactions of macroscopic adhesive bodies. We perform comprehensive molecular dynamics simulations and observe for all four potentials power-law dependencies for the size distribution of collision fragments and for their size-velocity correlation. We introduce a new fragmentation characteristic-the shattering degree S, quantifying the fraction of monomers in debris and reveal its universal behavior. Namely, we demonstrate that for all potentials, 1 − S is described by a universal function of the impact velocity. Using the above results, we perform the impact classification and construct the respective collision phase diagram. Finally, we present a qualitative theory that explains the observed scaling behavior.

Scaling laws for impact fragmentation of spherical solids

Physical Review E, 2012

We investigate the impact fragmentation of spherical solid bodies made of heterogeneous brittle materials by means of a discrete element model. Computer simulations are carried out for four different system sizes varying the impact velocity in a broad range. We perform a finite size scaling analysis to determine the critical exponents of the damage-fragmentation phase transition and deduce scaling relations in terms of radius R and impact velocity v 0 . The scaling analysis demonstrates that the exponent of the power law distributed fragment mass does not depend on the impact velocity; the apparent change of the exponent predicted by recent simulations can be attributed to the shifting cutoff and to the existence of unbreakable discrete units. Our calculations reveal that the characteristic time scale of the breakup process has a power law dependence on the impact speed and on the distance from the critical speed in the damaged and fragmented states, respectively. The total amount of damage is found to have a similar behavior, which is substantially different from the logarithmic dependence on the impact velocity observed in two dimensions.

Multifractality and the shattering transition in fragmentation processes

Physical Review E, 1996

We consider two simple geometric models that can describe the kinetics of fragmentation of two dimensional particles and stochastic fractals. We find a hierarchy of independent exponents suggesting the existence of multiple phase boundary for the shattering transition when two orthogonal cracks are placed randomly on a fragments (Model A). At the same time we find a unique exponent suggesting a single phase boundary when four equal sized fragments are produced at each fragmentation event (Model B). We invoke the multifractal formalism to further support the existence of multiple phase boundary. In model A, for each choice of homogeneity indices, the resultant fragments distribution exhibits multifractality on a unique support when describing fragmentation process and on one of infinitely many possible supports when describing stochastic fractals. The model B obeys simple scaling and produce self-similar fractals when fragments are removed from the system at each time step.

Multifractality of mass distribution in fragmentation

Physica A: Statistical Mechanics and its Applications, 2000

Fragmentation is studied using a simple numerical model. An object is taken to be two dimensional and consists of particles that interact pairwise via the Lennard-Jones potential while the e ect of the fragmentation-induced forces is represented by some initial velocities assigned to the particles. As time evolves, the particles form clusters which are identiÿed as fragments. The fragment mass distribution has been found to depend on the input energy. This energy dependence is investigated and the fragment mass distribution is found to be multifractal in that a single exponent is not su cient to characterize the energy dependence of the di erent moments of the mass distribution. We have further attempted to explore the interesting possibility that this multifractality of the fragment mass distribution might be a consequence of the properties of the object before it breaks up into many pieces.

A kinetic description of particle fragmentation

2000

This paper is concerned with the formulation and analysis of par- ticle fragmentation by a mathematical approach of the kinetic theory. We consider a fairly general model which may require a description of the internal configuration of each particle, like internal energy. The fragmentation process is supposed to occur due to the configuration of the corresponding particle; An easy modification