A Spectral Elastodynamic Method for Bi-material Interface Problems

A computational method is proposed for modeling spontaneous propagation of dynamic cracks and slip ruptures at a planar interface between two dissimilar elastic half-spaces. It is based on a spectral formulation of the boundary integral equation method and is suited to parallel computing. The boundary integral equation can be written in two equivalent forms: (a) The tractions can be written as a space-time convolution of the displacement continuities at the interface (b) The displacement discontinuities can be written as a space-time convolution of the tractions on the interface. Prior work on spectral formulation of the boundary integral equation has adopted the former as the starting point. The present work has for its basis the latter form based on a space-time convolution of the tractions. The radiation damping term is then explicitly extracted to avoid singularities in the convolution kernels. Stress and displacement components are given a spectral representation as finite Fourier series in the spatial coordinate along the interface. With the spectral forms introduced, the space-time convolutions are converted to convolutions in time for each Fourier mode. The distinguishing feature of the method is that elastodynamic convolutions are performed over the history of tractions on the interface. Due the continuity of tractions across the interface, this leads to a simpler formulation and form of the convolution kernels, as compared to existing methods. When coupled with a cohesive law or a friction law, the method is of wide applicability for studying spontaneous crack or slip rupture propagation. The limitations of the method are that it is restricted to planar interfaces and semi-infinite geometries.