Purusattam Ray

First-Order Transition in the Breakdown of Disordered Media

We study the approach to global breakdown in disordered media driven by increasing external forces. We first analyze the problem by mean-field theory, showing that the failure process can be described as a first-order phase transition, similarly to the case of thermally activated fracture in homogeneous media. Then we quantitatively confirm the predictions of the mean-field theory using numerical simulations of discrete models. Widely distributed avalanches and the corresponding meanfield scaling are explained by the long-range nature of elastic interactions. We discuss the analogy of our results to driven disordered first-order transitions and spinodal nucleation in magnetic systems. [S0031-9007(97)02501-5]

Avalanches in Breakdown and Fracture Processes

We investigate the breakdown of disordered networks under the action of an increasing external-mechanical or electrical-force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first-order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.

Statistics of fracture surfaces

We analyze the statistical distribution function for the height fluctuations of brittle fracture surfaces using extensive experimental data sampled on widely different materials and geometries. We compare a direct measurement of the distribution to an analysis based on the structure functions. For length scales delta larger than a characteristic scale Lambda that corresponds to a material heterogeneity size, we find that the distribution of the height increments Deltah=h(x+delta)-h(x) is Gaussian and monoaffine, i.e., the scaling of the standard deviation sigma is proportional to delta(zeta) with a unique roughness exponent. Below the scale Lambda we observe a deviation from a Gaussian distribution and a monoaffine behavior. We discuss for the latter, the relevance of a multiaffine analysis and the influences of the discreteness resulting from material microstructures or experimental sampling.

Finite-Size Effect in the Dynamics Near the Glass Transition

The dynamics near the glass transition in a two-dimensional lattice model of polymer melt is studied by Monte Carlo simulation. Mean-square displacements of the individual monomers as well as of the centres of mass of the polymers are observed for over seven decades of time which provide quite reliable equilibrated values (corresponding to the results from a quasi-static cooling measurement) of the diffusion constant. The diffusion constants are determined as a function of temperature and size of the lattice (keeping the density of the monomers and the degree of polymerization fixed). A striking size dependence is shown by the diffusion constant at low temperatures, which suggests the possibility of the existence of strongly cooperatively rearranging regions in the system, as was postulated by Adam and Gibbs. Our results indicate the increase of the mean size of such regions as the temperature is lowered.

A microscopic approach to the statistical fracture analysis of disordered brittle solids

Abstract The static fracture properties of disordered brittle solids, having ordered crystalline structure and a random distribution of flaws (broken bonds), are studied here from a microscopic point of view. In the weak disorder limit, starting from McClintocks description, we have obtained the empirical Weibull formula for the average fracture strength σ c , giving all its fitting parameters. The result of a molecular dynamic simulation of fracture in a square Lennard-Jones system, containing 400 atoms and randomly broken bonds, are found to compare very well with the theory.

Dispersity-Driven Melting Transition in Two Dimensional Solids

We perform extensive simulations of 10 4 Lennard-Jones particles to study the effect of particle size dispersity on the thermodynamic stability of two-dimensional solids. We find a novel phase diagram in the dispersity-density parameter space. We observe that for large values of the density there is a threshold value of the size dispersity above which the solid melts to a liquid along a line of first order phase transitions. For smaller values of density, our results are consistent with the presence of an intermediate hexatic phase. Further, these findings support the possibility of a multicritical point in the dispersity-density parameter space.

Statistical physics of fracture, breakdown, and earthquake : effects of disorder and heterogeneity

They explain fracture-like phenomena, highlighting the role of disorder and heterogeneity from a statistical physical viewpoint. The role of defects is discussed in brittle and ductile fracture, ductile to brittle transition, fracture dynamics, failure processes with tension as well as compression: experiments, failure of electrical networks, self-organized critical models of earthquake and their extensions to capture the physics of earthquake dynamics. The text also includes a discussion of dynamical transitions in fracture propagation in theory and experiments, as well as an outline of analytical results in fiber bundle model dynamics

Analysis of damage clusters in fracture processes

We present numerical simulations of two-dimensional models of electric breakdown and fracture in disordered systems subject to an increasing external stress. We provide a geometrical characterization of the damage by studying the scaling behavior of connected bonds clusters. The average cluster size and the lattice conductivity show features characteristic of a first order phase transition. The obtained results are discussed within the spinodal nucleation scenario recently proposed for fractures.

Nucleation versus percolation: Scaling criterion for failure in disordered solids.

One of the major factors governing the mode of failure in disordered solids is the effective range R over which the stress field is modified following a local rupture event. In a random fiber bundle model, considered as a prototype of disordered solids, we show that the failure mode is nucleation dominated in the large system size limit, as long as R scales slower than L(ζ), with ζ=2/3. For a faster increase in R, the failure properties are dominated by the mean-field critical point, where the damages are uncorrelated in space. In that limit, the precursory avalanches of all sizes are obtained even in the large system size limit. We expect these results to be valid for systems with finite (normalizable) disorder.

Spatial distribution of persistent sites

We study the distribution of persistent sites (sites unvisited by particles A) in the one-dimensional A + A→∅ reaction-diffusion model. We define the empty intervals as the separations between adjacent persistent sites, and study their size distribution n(k,t) as a function of interval length k and time t. The decay of persistence is the process of irreversible coalescence of these empty intervals, which we study analytically under the independent interval approximation (IIA). Physical considerations suggest that the asymptotic solution is given by the dynamic scaling form n(k,t) = s-2f(k/s) with the average interval size s~t1/2. We show under the IIA that the scaling function f(x)~x-τ as x→0 and decays exponentially at large x. The exponent τ is related to the persistence exponent θ through the scaling relation τ = 2(1-θ). We compare these predictions with the results of numerical simulations. We determine the two-point correlation function C(r,t) under the IIA. We find that for r<<s, C(r,t)~r-α where α = 2-τ, in agreement with our earlier numerical results.We study the distribution of persistent sites (sites unvisited by particles