Infinitesimal Deformation of a Body with a Finite Pre-stress
We devote this chapter to deriving the linearised equations and jump conditions that govern infinitesimal elastic deformations of a body initially in static equilibrium. The property of elasticity refers only to incremental deformations, while the state of initial stress may be due to any physical cause. Here, we consider that the initial static stress is caused by self-gravitation, that is, the gravitational forces acting between the material particles of a body. The principal assumption is that the initial static stress caused by self-gravitation is accounted for in a self-consistent treatment of a gravitating body with a three-dimensional density structure.