Higher order weight functions in fracture mechanics of inhomogeneous anisotropic solids

Abstract

A two-dimensional theory of higher-order weight functions is developed for inhomogeneous anisotropic elastic solids with notches or cracks. Elasticity constants have an arbitrary angular dependence around the notch (crack) tip. Specimens of finite size and arbitrary geometry, subjected to both surface displacements and tractions, are considered. The theory allows the computation of a complete set of expansion coefficients for the stress field into a series over the infinite notched elastic plane eigenfunctions. The approach used is based on the Bueckner concept of regular and fundamental fields, to which the reciprocity theorem is applied to obtain the expansion coefficients.