eFunda: The J Integral
 The J Integral
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 Definition of J Integral 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
 J vs. and K For linear elastic materials, the J integral J is in fact the strain energy release rate, , and both are related to the stress intensity factor K in the following fashion: