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) PACS numbers: 05.70. Ln, 62.20.Mk, 64.60.Fr The breakdown of solids under external forces is a longstanding problem that has both theoretical and practical relevance [1]. The first theoretical approach to fracture mechanics, proposed by Griffith [2] more than 75 years ago, is similar to the classical theory of nucleation in firstorder phase transitions [3]. An elastic solid under stress is in a "metastable state" and will decay to the "stable fractured state" by the formation of cracks. Recently it has been shown [4] that the point of zero external stress has the same mathematical properties as the condensation point in gas-liquid first-order transitions. In the language of phase transitions, the stress imposed on the solid plays the role of an external field and cracks are the analog of droplets of a new phase. The classical theory of nucleation is expected to fail close to the limit of stability, the spinodal point [5], and it has been suggested [6-9] that a similar behavior should occur for fracture, for large values of the external stress. Thus, the failure threshold corresponds to the spinodal point of first-order phase transitions.The Griffith theory and related calculations deal with the situation in which fracture is thermally activated and quenched disorder is absent or weak. In many realistic situations, however, the solid is not homogeneous, and disorder, in the form of vacancies or microcracks, strongly affects the nucleation process [8,9]. There are situations, encountered, for example, in material testing, in which the system is driven by an increasing external stress [11] and the time scale of thermal fluctuations is much larger than the time scale induced by the driving. In those cases, the system can be effectively considered as being at zero temperature, so only quenched disorder is relevant. It has been experimentally observed [10][11][12][13][14] that the response (acoustic emission) of stressed disordered media takes place in bursts of widely distributed intensity, indicative of an internal avalanche dynamics.The understanding of the breakdown of disordered systems has considerably progressed due to the use of large scale simulations of lattice models [15]. These models have provided a good description of geometrical and topological properties of cracks, leading to the introduction in this f...

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We analyse 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 a new analysis based on the structure functions. For length scales δ larger than a characteristic scale δ * , we find that the distribution of the height increments ∆h = h(x + δ) − h(x) is Gaussian. Self-affinity enters through the scaling of the standard deviation σ, which is proportional to δ ζ with a unique roughness exponent. Below the scale δ * we observe an effective multi-affine behavior of the height fluctuations and a deviation from a Gaussian distribution which is related to the discreteness of the measurement or of the material.

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We investigate the breakdown of disordered networks under the action of an increasing externalmechanical 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.