Static solution of a crack degenerated from dynamic solution of a propagating crack
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A two-dimensional planar crack which propagates along its self-plane is taken as the fault model. The static solution of the classic (linear elastic fracture mechanics) model for this study for three types of two-dimensional cracks are obtained by means of degeneration method based on the dynamic solution obtained by Kostrov (1975). The degeneration method used in this study has two points of convenience: 1 One can obtain the solutions of different types of cracks by using the unified method; 2 It is avoided to use displacement potential and stress function which physical meaning is not straight. The results obtained in this paper are just the same as that obtained by previous authors who solved the equilibrium equations by means of integral transform method. It is showed that: 1 The static solution cannot be separated from the dynamic one, because the static solution also has the meaning of duration time. 2 Both the static and the dynamic solutions of a critical crack must satisfy the same criteria, and the evolution from static to dynamic solution must be associated with some additional disturbance. Particularly, the quantity of disturbance in some form has to be imposed when a critical crack is ready to initiate.
Key wordsdynamics of earthquake rupture critical crack static solution degeneration method
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