A new spectral boundary integral equation method for antiplane problems

The spectral boundary integral equation (SBIE) method is widely used for numerical modeling of earthquake ruptures at a planar interface between two elastic half-spaces. It was originally proposed by Geubelle and Rice (1995) based on the boundary integral formulation of Budiansky and Rice (1979). The distinguishing feature of the formulation is that it involves performing elastodynamic space-time convolution of the displacement discontinuities at the interface between the two solids. The method was extended to bi-material interfaces by Geubelle and Breitenfeld (1997) and Breitenfeld and Geubelle (1998). An alternative boundary integral formulation to that of Budiansky and Rice (1979) is that of Kostrov (1966), where the elastodynamic space-time convolution is done of the tractions at the interface between the two solids. A SBIE method based on the latter formulation was proposed by Ranjith (2015) for plane strain. In the present work, the SBIE method for antiplane strain based on the formulation of Kostrov (1966) is proposed and compared with other approaches. Illustrations of the use of the method for simulating dynamic antiplane ruptures at bi-material interfaces are given.