Weight function theory and variational formulations for three-dimensional plane elastic cracks advancing

The weight function theory for three-dimensional elastic crack analysis received great attention after the
work of Rice (1985, 1989). Several applications have been considered since then, particularly in the context
of configurational stability, crack path prediction, stress intensity factor expansions, perturbation
approaches. In all cases, a specific hypothesis has been made on the variation of crack shape, in order
to formulate the problem in terms of Cauchy principal value. In the present note, such hypothesis is further
investigated and consequences discussed. A variational statement given in Salvadori and Fantoni
(2013a) is thus rephrased in terms of weight functions. Its discrete formulation shows the potential to
accurate approximation of crack front propagation.