A dislocation and point force approach to the boundary element method for mixed mode crack analysis of plane anisotropic solids

Abstract

In this paper we formulate a direct boundary element method (BEM) for plane anisotropic elasticity (i.e., the in‐plane deformation decoupled from the out‐of‐plane deformation) based on distributions of point forces and dislocation dipoles. According to a physical interpretation of Somigliana's identity the displacement field in a finite body R is represented by the continuous distributions of point forces and dislocation dipoles along the imaginary boundary ?R of the finite domain R embedded in an infinite body. We adopt Stroh's complex variable formalism for anisotropic elasticity and represent the point force and the dislocation, their dipoles, and continuous distributions systematically exploiting the duality relations between the point force and the dislocation solutions. Explicit formulas for the displacement and the traction formulations, obtained by analytical integration of the boundary integrals, are given. We apply these formulas to mixed mode crack problems for multiply cracked anisotropic bodies by extending the physical interpretation of Somigliana's identity to cracked bodies and representing the crack by the continuous distribution of dislocation dipoles. With the help of the conservation integrals of anisotropic elasticity, we will demonstrate the capability of the method to determine the mixed mode stress intensity factors (K_I and K_II ) accurately.