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Consider a nonlinear elastic body containing a crack,
the J integral is defined as
where  is the strain energy density,  is the traction vector,  is an arbitrary contour around the tip of the crack, n is the unit vector normal to ;  ,  , and u are the stress, strain, and displacement field, respectively.
Rice, J. R., 1968, showed that the J integral is a path-independent line integral and it represents the strain energy release rate of nonlinear elastic materials:
where  is the potential energy, the strain energy U stored in the body minus the work W done by external forces and A is the crack area.
The dimension of J is
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and K
