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Crack in an Arbitrary Body
A general formula for determining the J integral of a crack in an arbitrary body is described in this section.

For a nonlinear elastic body containing a crack along xi axis, the J integral, from the definition, is

or alternatively, J can be rewritten in a matrix form,


for plane strain and for plane stress.

The J intergral can be expanded in terms of the global x-y coordinates as after change of variables: