ABSTRACT
This chapter presents classical notions of elasticity theory and introduces stress, which is of a mechanical nature, as distinct from the geometrically defined displacement and deformation. The derivation of equations of motion is based on the assumption that any volume chosen within an elastic medium can be regarded as a mechanical system, the motion of which can be described on the basis of the Hamilton principle. Equations describing the dynamics of elastic media can easily be obtained by applying the second Newton law to an infinitely small volume. The chapter deals with an elementary volume in the medium of which the properties are continuously varying. It focuses on wave processes on the boundary of an elastic medium and on the interface between two physically different media. The chapter presents several reasonable boundary conditions, discussing from the Lagrangian point of view.
