Elastodynamics of Failure in a Continuum
A general treatment of the elastodynamics of failure in a prestressed elastic continuum is given, with particular emphasis on the geophysical aspects of the problem. The principal purpose of the study is to provide a physical model of the earthquake phenomenon, which yields an explicit description...
| Summary: | A general treatment of the elastodynamics of failure in a
prestressed elastic continuum is given, with particular emphasis on the geophysical aspects of the problem. The principal purpose of the study is to provide a physical model of the earthquake phenomenon, which yields an explicit description of the radiation field in terms of source parameters.
The Green's tensor solution to the equations of motion in a medium with moving boundaries is developed. Using this representation theorem, and its specialization to the scalar case by means of potentials, it is shown that material failure in a continuum can be treated equivalently
as a boundary value problem or as an initial value problem. The initial value representation is shown to be preferable for geophysical purposes, and the general solution for a growing and propagating rupture zone is given.
The energy balance of the phenomenon is discussed with particular emphasis on the physical source of the radiated energy. It is also argued that the flow of energy is the controlling factor for the propagation and growth of a failure zone. Failure should then be viewed as a generalized phase change of the medium.
The theory is applied to the simple case of a growing and propagating spherical failure zone. The model is investigated in detail both analytically and numerically. The analysis is performed in the frequency domain and the radiation fields are given in the form of multipolar expansions. The necessary theorems for the manipulation of
such expansions for seismological purposes are proved, and their use discussed on the basis of simple examples.
The more realistic ellipsoidal failure zone is investigated. The static problem of an arbitrary ellipsoidal inclusion under homogeneous stress of arbitrary orientation is solved. It is then shown how the
analytical solution can be combined with numerical techniques to yield more realistic models.
The conclusion is that this general approach yields a very flexible model which can be adapted to a wide variety of physical circumstances. In spite of the simplicity of the model, the predicted radiation field is rather complex; it is discussed as a function of source parameters, and scaling laws are derived which ease the interpretation of observed spectra. Preliminary results in the time domain are also shown. It is concluded that the model can be compared favorably both with the observations, and with results obtained from purely numerical models. |
|---|