The dual boundary element method: Effective implementation for crack problems

TLDR

The paper addresses efficient numerical implementation of the two‑dimensional dual boundary element method for linear elastic crack problems, using displacement and traction boundary integral equations applied on opposite crack surfaces to solve mixed‑mode crack problems in a single‑region formulation. The method discretizes both crack surfaces with discontinuous quadratic boundary elements, automatically satisfying finite‑part integral conditions and avoiding collocation problems at crack tips, kinks, and corners, and is applied to geometries with edge and embedded cracks. The approach yields highly accurate stress intensity factors via the J‑integral, and its accuracy and efficiency make it well suited for studying crack growth under mixed‑mode conditions.

Abstract

Abstract The present paper is concerned with the effective numerical implementation of the two‐dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed‐mode crack problems can be solved with a single‐region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite‐part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack‐edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J ‐integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed‐mode conditions.