Dual boundary element method for analyzing three-dimensional cracks in layered and graded halfspaces

This paper presents a dual boundary element analysis of three-dimensional cracks in layered and graded halfspaces. The fundamental solution of a multilayered solid is used to develop the dual boundary element method so that only the external boundary surface and the crack surface need to be discretized while the material interfaces do not need to be discretized. Infinite boundary elements and crack-tip discontinuous elements are introduced to consider the far-fields of a layered halfspace and capture the crack-tip behavior, respectively. Special attentions are given to strongly singular and hypersingular integrals in the discretized displacement and traction boundary integral equations. For square-shaped, penny-shaped and elliptical cracks located in a homogeneous halfspace, the stress intensity factors obtained with the present formulation are in very good agreement with existing numerical results and closed-form solutions. The square-shaped cracks in horizontally layered halfspaces and the penny-shaped and elliptical cracks in graded halfspaces are analyzed. Results show that the material heterogeneity in layered and graded halfspaces can have a profound effect on the stress intensity factors.