Scaling and dimensional analysis

Abstract

The fundamental concepts necessary to understand soft impact will be presented in this and the next chapter. First, definitions of unit, dimension, stress, and strain are introduced. Then, the basic ideas of scaling and dimensional analysis are briefly explained on the basis of fundamental continuum mechanics. After reviewing the elementary theory of the fluid drag force, a list of meaningful dimensionless numbers is provided. Finally, the concept of the similarity law, which is important in the design and analysis of the experimental system, is described. In the next chapter, constitutive laws of soft matter particularly for granular matter are intensively discussed. Because this and the nextchapters concern fundamentals, those who already have a good understanding of continuum mechanics and granular matter do not need to read these chapters. Note that, however, many equations derived in these chapters will be used in the subsequent chapters.