JMAN : J-integral calculation

The J-integral is a way to calculate the energy released propagating a crack per unit area. The value of calculated J-integral is theoretically independent from the chosen contour, provided that the material is elastic.

We will see how in JMAN we calculate the J-integral value from a displacement field.

The input data are the results of digital image correlation analysis or the results of a finite elements calculation. The input requires the 2D coordinates of the points at which measurements (or calculations) were performed along with the respective 2D displacement values.

The first step is to create a finite element mesh were the input values are the values at the nodes of our mesh.

Fig 1. Mesh of quadratic elements

Once this mesh is created, we will calculate the stress and strain values at the integration points. From those results, a contributive term for J at each element in the chosen contour is determined.

Fig 2. Example of a J-integral contour

The final step is to retrieve the J-integral value by summing the J contributive terms of each element in the contour.
The value of K, the stress intensity factor is easily determined from the value of J.