Boundary integral spectral formulation for in-plane rupture propagation at non-planar bi-material interfaces

The effect of heterogeneity (dissimilar materials) and geometry constituting an interface is an important problem in earthquake source mechanics. These two parameters in the fault interface are responsible for complex rupture propagation and instabilities compared to the homogeneous planar interface. Here, a boundary integral spectral method (BISM) is proposed to capture the in-plane rupture propagation in the non-planar bi-material interface. The conventional traction BISM suffers from the disadvantages of hyper singularity and regularisation is needed (Sato et al., 2020; Romanet et al., 2020; Tada and Yamashita, 1997). So, we are utilising the representation equation arising from the displacement formulation devised by Kostrov (1966). It uses the elastodynamic space-time convolution of Green’s function and traction component at the interface. These displacement boundary integral equations (BIEs) are the inverse equivalent of traction BIEs. When applied to an interface between heterogeneous planar elastic half-spaces, these displacement BIEs have yielded simple and closed-form convolution kernels (Ranjith 2015; Ranjith 2022). Displacement BIEs of this kind have not been utilised to analyse fracture simulation for non-planar bi-material interfaces until now. We assume the small slope assumption (Romanet et al., 2024) in our formulation to get the required displacement BIEs. Also, we expand the displacement BIEs of a non-planar bi-material interface to the leading order to obtain the non-planarity effects. Finally, we present a general spectral boundary integral formulation for a non-planar bi-material interface independent of specific geometry and traction distribution in a small fault slope regime.