Dimensional Analysis of Critical Phenomena: Self-Weight Failure, Turbulence, Resonance, Fracture
Alberto Carpinteri, Federico Accornero
Abstract
Both in physics and engineering, Buckingham’s Π theorem is considered as a key tool for dimensional analysis, providing a method to identify the dimensionless parameters governing physical similitude and scale modeling, when the form of the solving equations is still unknown. In the present paper, the scaling of different critical phenomena in solid and fluid mechanics is emphasized by the application of the Π theorem. In particular, self-weight failure, turbulence, resonance, and fracture are considered, highlighting how these critical phenomena are governed by specific dimensionless numbers, which are functions of few fundamental mechanical quantities including the size-scale, which are characterized by different and algebraically independent physical dimensions.