Dimensional Analysis of Critical Phenomena: Self-Weight Failure, Turbulence, Resonance, Fracture

Abstract: Both in physics and engineering, Buckingham’s Π theorem is considered as a keytool for dimensional analysis, providing a method to identify the dimensionlessparameters governing physical similitude and scale modeling, when the form ofthe solving equations is still unknown. In the present paper, the scaling ofdifferent critical phenomena in solid and fluid mechanics is emphasized by theapplication of the Π theorem. In particular, self-weight failure, turbulence,resonance, and fracture are considered, highlighting how these criticalphenomena are governed by specific dimensionless numbers, which are functions offew fundamental mechanical quantities including the size-scale, which arecharacterized by different and algebraically independent physicaldimensions.