Antiplane spectral boundary integral equation method for an interface between a layer and a half-plane

A numerical scheme is proposed for simulating dynamic antiplane fracture at an interface be-tween a layer and a half-plane. The scheme is a spectral boundary integral equation method which relates the shear stress and the displacement discontinuity at the interface in the spectral domain. In previous studies, numerical schemes have been developed for fracture problems in unbounded solids. This is the first work where a spectral boundary integral equation method has been developed for a system one of whose constituents is a finite solid, namely, a layer. The spectral scheme involves performing time convolution of the spectral amplitude of the shear stress at the interface of the layer and half-space. Numerically, conversion between the spectral domain and spatial domain is done by the Fast Fourier Transform. The numerical scheme is validated through comparison with known solutions of model problems. Use of the numerical method is illustrated by simulating 2D antiplane slip rupture propagation wherein the spectral boundary integral equation is coupled with a slip-weakening friction law. We illustrate the role of initial stress distribution on the modes of rupture propagation at the interface, which can be crack-like or pulse-like. The effect of the layer thickness on the critical nucleation size for dynamic rupture propagation is also studied numerically.