ABSTRACT
This chapter deals with static (time-independent) elasticity involving homogeneous deformations. It introduces 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. The condition of static equilibrium leads to symmetry of the stress tensor. The tensile stresses along any one axis must balance; otherwise, the body would accelerate, so that there can only be three independent diagonal stresses. Likewise, the shear stresses must balance to avoid rotation, leading to three off-diagonal stresses. In its simplest form, Hooke’s law states that for small elongations of an elastic system, the stress is proportional to the strain.
