The J-integral may be calculated directly using the finite element mesh and shape functions. We consider a domain contour as shown in figure 4 and choose an arbitrary smooth function q ~ ~ ( x 1 , x 2 ) = ∑ ∑ i N i ( x 1 , x 2 ) q ~ ~ i such that q ~ ~ = 1 on Γ Γ and q ~ ~ = 0 on C 1 .