J-integral
![](/Images/godic/202501/21/BernoullisLawDerivationDiagram.svg0608.png")
![Figure 1. Line J-integral around a notch in two dimensions.](/Images/godic/202501/21/Integrale-J_2D0608.png")
![Figure 2. Integration paths around a notch in two dimensions.](/Images/godic/202501/21/J_integralPathIndep0609.png")
![Paths for J-integral calculation around a notch in a two-dimensional elastic-plastic material.](/Images/godic/202501/21/HRRSingularity_plain.svg0609.png")
The J-integral represents a way to calculate the strain energy release rate, or work (energy) per unit fracture surface area, in a material. The theoretical concept of J-integral was developed in 1967 by Cherepanov and in 1968 by Jim Rice independently, who showed that an energetic contour path integral (called J) was independent of the path around a crack.