The 3-D weight functions for a quasi-static planar crack

We explicitly evaluate the 3-D weight functions for a planar crack in an is otropic, homogeneous material; these give the full stress intensity factors induced by a static point force applied at an arbitrary position. If we Fo urier decompose the 3-D weight functions with respect to the z variable the n each Fourier mode satisfies the homogeneous equations of elasticity (exce pt at the crack tip) and the boundary conditions on the crack face. Each Fo urier mode diverges like r(-1/2) near the crack tip and decays exponentiall y for non-zero k(z). It is proved that these necessary conditions, which ho ld everywhere in the elastic material excluding the crack tip, are also suf ficient to determine the 3-D weight functions. In particular, the 3-D weigh t functions can be calculated without considering an explicit loading probl em. (C) 2000 Elsevier Science Ltd. All rights reserved.