ABSTRACT
The theory of elasticity is the study of the mechanics of continuous media, or in simple words, the deformation of the elements of a solid body by applied forces. In this chapter we deal with static (time independent) elasticity involving homogeneous deformations. In fact, the parameters defined here can also be used at the finite frequencies occurring in ultrasonic propagation. This is the simplest case and enables us to define concepts such as deformation, strain tensor, stress tensor, and the moduli of elasticity. We introduce tensor notation to describe the elastic parameters; it is a simple, elegant, and powerful approach that is used throughout advanced treaties in elasticity and acoustics. Complete discussions are given for tensors by Nye [11] and for elasticity by Landau and Lifshitz [12].
