Analysis of crack problems in multilayered elastic medium by a consecutive stiffness method

Abstract

We propose a boundary-element-based method for crack problems in multilayered elastic medium that consists of a set of individually homogeneous strata. The method divides the medium along the slit-like crack surface so that the effects of the elements placed along one crack surface become distinguishable from those placed along the other surface. As a result, the direct method that cannot be directly applied for crack problems turns out to be applicable. After that, we derive a recursive formula that obtains a “stiffness matrix” for each layer by exploiting the chain-like structure of the system, enabling a sequential computation to solve the displacements on the crack surface in each layer “consecutively” in a descending order from the very top layer to the very bottom one. In our method, the final system of equations only contains the unknown displacements on the crack surface, ensuring the efficiency of the method. The numerical examples demonstrate better accuracy and broader applicability of our method compared to the displacement discontinuity method and more-acceptable efficiency of our method compared to the conventional direct method.