Incremental Statics and Dynamics of Pre-Stressed Elastic Materials

In this chapter we provide a summary of the equations governing the incremental deformations superimposed on a finite deformation of an elastic solid. For the equilibrium equations the incremental theory is built on top of the underlying finite deformation theory, which includes discussion of constitutive laws for isotropic materials and for anisotropy associated with one or two preferred directions. Following the static theory the corresponding dynamic equations are summarized. The resulting equations for incremental motions superimposed on a static finite deformation are then used to examine some basic problems in the propagation of incremental plane waves in pre-stressed elastic solids in order to illustrate the influence of the pre-stress and the associated finite deformation on the wave propagation characteristics.