A numerical method for determination of source time functions for general three-dimensional rupture propagation

Abstract

We present a method to determine the displacement and the stress on the crack plane for a truly three-dimensional shear crack of arbitrary shape propagating in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane. The main idea of the method (which is due to Hamano) is to use a representation theorem in which the displacement at any given point on the crack plane is written as an integral of the traction over the whole crack plane. The tractions are weighted by the three-dimensional solution to Lamb's problem. Such solutions usually require one numerical integration, but fortunately the necessary solutions are obtainable in closed form. The weighting factor is discretized over a space and time grid to solve the integral equation numerically. As a test of the accuracy of our numerical technique, we compare the results with known solutions for two simple cases.