A contour that does not care which path you take
Rice’s J is the energy released per unit area of crack advance. On any path around the tip it equals KI²/E for a linear elastic plate in plane stress. The same integral, taken around the tip of a rigid line inclusion, measures the configurational force on that tip. At the mechanically neutral orientation the far field is unperturbed, the tip intensities vanish, and J is zero.
J vs contour radius
J = ∮ (w nx − t · ∂u/∂x) dΓ
Colour is σyy near the tip. On a crack, change the contour radius: the discrete line integral stays at KI²/E. On a rigid line, turn θ: J vanishes at θn = arctan(1/√ν).