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.