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.

中文翻译：

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临界现象的量纲分析：自重失效、湍流、共振、断裂

摘要

在物理学和工程学中，白金汉 Π 定理被认为是量纲分析的关键工具，当求解方程的形式仍然未知时，它提供了一种方法来识别控制物理相似和尺度建模的无量纲参数。在本文中，通过 Π 定理的应用，强调了固体和流体力学中不同临界现象的标度。特别地，考虑了自重破坏、湍流、共振和断裂，突出了这些关键现象是如何受特定无量纲数控制的，这些无量纲数是包括尺寸尺度在内的少数基本力学量的函数，具有不同的代数特征独立的物理尺寸。