Spectral formulation of the boundary integral equation method for antiplane problems

TL;DR

This paper introduces a spectral formulation of the boundary integral equation method for antiplane problems, enhancing numerical efficiency by performing convolutions in the spectral domain and applying it to interface response and slip rupture simulations.

Contribution

It develops a spectral boundary integral method focusing on shear stress convolution, extending prior work that only considered slip, and applies it to dynamic rupture simulations.

Findings

Spectral formulation improves computational efficiency.

Validated against analytical solutions for harmonic and impulsive disturbances.

Successfully simulated slip rupture propagation with slip-weakening friction law.

Abstract

A spectral formulation of the boundary integral equation method for antiplane problems is presented. The boundary integral equation method relates the slip and the shear stress at an interface between two half-planes. It involves evaluating a space-time convolution of the shear stress or the slip at the interface. In the spectral formulation, the convolution with respect to the spatial coordinate is performed in the spectral domain. This leads to greater numerical efficiency. Prior work on the spectral formulation of the boundary integral equation method has performed the elastodynamic convolution of the slip at the interface. In the present work, the convolution is performed of the shear stress at the interface. The spectral formulation is developed both for an interface between identical solids and for a bi-material interface. It is validated by numerically calculating the response of the interface to harmonic and to impulsive disturbances and comparing with known analytical solutions. To illustrate use of the method, dynamic slip rupture propagation with a slip-weakening friction law is simulated.