Models and Measures of Statistical Physics and Sociophysics for Fracture Mechanics and Earthquake Dynamics: An Introduction

RESUMO

The breaking or fracture of materials and damages or devastations due to earthquakes have caught our attention since the earliest stage of human civilization. In fact, at around 1500, Leonardo Da Vinci made the pioneering observation that, unlike elastic constants (formalized later by Hooke in 1678) of the materials, the tensile (breaking) strengths of nominally identical iron wires decrease drastically with their length, indicating the vanishing breaking strength of materials in the large size limit, suggesting the impossibility of constructing arbitrarily large structures. This was the first observation that unlike the elasticity of disordered materials, which remains defined in the thermodynamic limit (self averaging statistics), the breaking properties of the disordered materials have extreme (non self averaging) statistics. In spite of major and some precise developments in statistical physical modelling and characterizing the fracture mechanics (starting with Allan Griffith's crack nucleation theory in 1921 and the weakest link failure Fibre Bundle Model of Frederick Thomas Peirce in 1926) and of earthquake dynamics (starting with Robert Burridge and Leon Knopoff's continuum dynamical model in 1967 and later other discrete or lattice train models or fractal overlap models of stick slip earthquakes), no graduate level textbook in condensed matter physics or in statistical physics introduces the basic models and their properties. And now computer scientists and social scientists (coming with their social inequality measures applied to the avalanche statistics in precursor failures) are joining their efforts to explore the new precursory inequality measures for big avalanches or failures. This introductory review is designed to fill this gap with a view to introducing these to this wider audience and to take them to the current frontiers in these fields.