Linear Anisotropic Elastic Materials

Abstract

The mechanical properties of materials are described by constitutive laws. There are a wide variety of materials existing in the world. We are not surprised that there are a great many constitutive laws describing an almost infinite variety of materials. What is surprising is that a simple idealized stress–strain relationship gives a good description of the mechanical properties of many elastic materials around us. In this chapter, we present the relation between stresses and strains in a linear anisotropic elastic material. By this relation, we need 21 elastic constants to describe a linear anisotropic elastic material if the materials do not possess any symmetry properties. In engineering application, this number is somewhat higher than expected. Consideration of the material symmetry will then reduce the number of elastic constants. To provide these constants obvious physical interpretation, engineering constants such as the Young’s moduli, Poisson’s ratios and shear moduli as well as some other behavior constants will also be introduced in this chapter. If the problems considered can be treated as a two-dimensional problem, the elastic constants needed for the analysis of the mechanical behavior of anisotropic materials can be further reduced.