Abstract
If one applies tensile stress on a solid, the solid elongates and gets strained. The stress (σ) – strain ( ε) relation is linear for small stresses (Hooke’s law) after which nonlinearity appears in most cases. Finally at a critical stress σf, depending on the material, amount of disorder, the specimen size, etc., the solid breaks into pieces; fracture occurs. In the case of brittle solids, the fracture occurs immediately after the Hookean linear region, and consequently the linear elastic theory can be applied to study the essentially nonlinear and irreversible static fracture properties of brittle solids [1]. With extreme perturbation, therefore, the mechanical or electrical properties of solids tend to get destabilised and failure or breakdown occurs. In fact, these instabilities in the solids often nucleate around disorder, which then plays a major role in the breakdown properties of the solids. The growth of these nucleating centres, in turn, depends on various statistical properties of the disorder, namely the scaling properties of percolating structures, its fractal dimensions, etc. These statistical properties of disorder induce some scaling behaviour for the breakdown of the disordered solids [2, 3].
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Chakrabarti, B. (2006). Statistical Physics of Fracture and Earthquake. In: Bhattacharyya, P., Chakrabarti, B.K. (eds) Modelling Critical and Catastrophic Phenomena in Geoscience. Lecture Notes in Physics, vol 705. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-35375-5_1
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