Framework of the classical theory of elasticity

Abstract

As the knowledge of crystals is a benefit for understanding quasicrystals, it is worth-while having a concise review of the classical theory of elasticity before learning the elasticity of quaicrystals. Here is a brief description to the theory. The detailed material for this theory can be found in many monographs and textbooks, e.g. Landau and Lifshitz[1]. Though the discussion here is limited within the framework of continuum medium mechanics, there are still connections to physical nature of the elasticity of crystals reflected by phonon concept (discussed in Section 1.5). The readers are advised to refer to the relevant chapters and sections of monographs of Born and Huang[2] and Anderson[3] which would help us understanding the phonon concept so the phason concept and elasticity of quasicrystals, which will be presented in the following chapters. The practice shows that it would be hard to understand phason concept and the phason elasticity if we limited our knowledge only within the classical continuum medium and complete intuition.