Development of dynamic slip model for a shear crack

The objective of this paper is to develop a dynamic slip model for a shear crack under constant stress drop. This crack problem is formulated by a traction boundary integral equation (BIE) in the frequency domain and then solved by the hyper-singular boundary element method as well as the regularization technique proposed in this paper. Based on the spectral integral form of the kernel function, the unbounded term can be isolated and extracted from the hyper-singular kernel function by using the method of subtracted and added back in wave number domain. Finally, based on the inverse transformation from the frequency domain to the time domain, the time histories of crack opening displacement under constant stress drop can be determined. Three rupture models (simultaneous rupture model, symmetric bilaterally-propagating model and unilaterally propagating model) with specified time histories of stress drop are considered in this paper. Even though these three models will cause the same final slip shapes because of the same constant stress drop, the associated slip time functions differ significantly from each other during the rupture process.