Spectral boundary integral equation method for simulation of 2D and 3D slip ruptures at bi‐material interfaces

Abstract

AbstractThis paper presents a 3D spectral numerical scheme that can accurately model planarcracks of any shape residing on an interfacial plane between two elastic solids. The cracks propagate dynamically under the action of interfacial loads and interfacial constitutive laws. The scheme is a spectral form of the boundary integral equations (BIE) that relate the displacement discontinuity fields along the interfacial plane to the stress fields at the plane. In the BIE, the displacement discontinuities are expressed as a spatio‐temporal convolution of the traction components at the interface. This is in contrast with most previous studies which use a spatio‐temporal convolution of the displacement discontinuities or of the displacements at the interface. Due to the continuity of tractions across the interface, the present formulation is simpler, resulting in convolution kernels that can be written in closed‐form. Previous studies have relied on numerically obtained convolution kernels. The accuracy of the proposed scheme is validated with the known analytical solution of the 3D Lamb problem. Furthermore, new algorithms are developed for coupling the BIE with a slip‐weakening friction law, both for homogeneous materials as well as for bi‐material interfaces. This results in a widely applicable formulation for studying spontaneous rupture propagation. The algorithms are validated by comparing rupture simulation exercises to benchmark problems from Southern California Earthquake Center (SCEC). Finally, the methodology is used to simulate 3D frictional rupture propagation along a bi‐material interface.