Mixed Mode I,II and III analysis of multiple cracks in plane anisotropic solids by the BEM: a dislocation and point force approach

A direct boundary element method (BEM) for plane anisotropic elasticity is formulated for the generalized plane strain. It deals with the general case when the in-plane and out-of-plane deformations are coupled, including the special case when they are decoupled. The formulation is based on the distributions of point forces and dislocation dipoles following the physical interpretation of Somigliana's identity. We adopt Lekhnitskii-Eshelby-Stroh formalism for anisotropic elasticity and represent the point force and the dislocation, their dipoles, and continuous distributions systematically; the duality relations between the point force and the dislocation solutions are fully exploited. The analytical formulas for the displacement and the traction BEM are applied to the mixed mode crack analysis for multiply cracked anisotropic bodies. We extend the physical interpretation of Somigliana's identity to cracked bodies and represent the crack by the continuous distribution of dislocation dipoles. The mixed mode stress intensity factors (K_I, K_II and K_III) are determined accurately with the help of the conservation integrals of anisotropic elasticity.