applied fracture mechanics

Higher Order Weight Functions in Fracture Mechanics of MultimaterialsHigher Order Weight Functions in Fracture Mechanics of Multimaterials 57x 2(r,ω)321n-2n-1ΩnS Nx 1Figure 2. Multimaterial consisting of n bonded together elastic wedges with different elastic constantsC (m)ijkl ,(m = 1,...,n). S Nx 1x 2(r,ω)n 0mnm 0C ijkl (ω)ΩFigure 3. Elastic plane with a notch and the elastic constants C ijkl (ω) continuously dependent on theazimuth ω. Basis (m,n,t) is rotated counterclockwise by an angle ω against a fixed basis (m 0 ,n 0 ,t).anisotropic media can be found in [16] and [23, 24], respectively. The consistency equation wasfurther applied in [29] to study the stress behavior in the angularly inhomogeneous elasticwedges near and at the critical wedge angle.4. Eigenfunction expansionsAccording to [28], an extension of the Williams’ eigenfunction expansion [1] to the notchedbody shown in Fig. 3 can be constructed from homogeneous solutions of Eq. (11). A suitable