A Combined Boundary Integral Method for Analysis of Crack Problems in Multilayered Elastic Media

Abstract

An efficient and accurate elastic analysis based on boundary integral methods is presented for crack problems in inhomogeneous elastic media consisting of a set of individually uniform strata. The method combines the direct boundary integral method (DM) and the displacement discontinuity method (DDM) so that it shares both the efficiency of the DDM and the broad applicability of the DM. The DDM is implemented to construct the stiffness matrix in each layer, while the DM is used to characterize the effects of the interfaces. All the variables on the interfaces can then be eliminated through the continuity conditions, leading to the final system of equations consisting of variables on crack surfaces only. The concept of the crack tip element is also adopted for a better treatment of the crack tip singularity. The examples demonstrate that the combined method has comparable accuracy of DM but is more efficient, especially for the scaled thin layers in the application of practical hydraulic fracturing simulations.