Elastic Dislocation Theory for a Self-Gravitating Elastic Configuration with an Initial Static Stress Field II. Energy Release

Three types of energy must be considered in a discussion of the energy distribution in the infinitesimal dynamic elastic-gravitational deformations of a uniformly rotating, self-gravitating, elastic configuration with a possibly large, anisotropic initial static stress: thermodynamic elastic internal energy, gravitational potential energy, and kinetic energy. Suitable expressions for these three types of energy are deduced, and are used to construct a Lagrangian from which the possible deformations of the system may be found by the principle of least action. The net energy change resulting from the introduction of a kinematically prescribed static tangential displacement dislocation is determined, and is shown to be very similar to the traditional expression first used by Reid, even though the theory is developed in such a way that the initial static stress is not necessarily assumed to arise from an initial elastic strain away from some natural stress-free configuration.