**test

Description

This command is used for calculating the \(J\) integral or \(\Delta J\) using a line set only. The command will work in 2D plane stress and plane strain only. Any material may be used, and any standard mechanical element formulation.

The integral is evaluated by performing direct integration of the contour integral

(99)\[J = \int_\Gamma \left[ W n_x - \sigma_{ij}n_j \pder{\bf u}{x}\right]d\Gamma\]

The calculation will be negative if the path is oriented clockwise. Also, remember that if there is a plane of symmetry about the crack plane, and you only model this one half, the associated \(J\) integral will be one half of its real value.

Syntax

The syntax for this output command is the following:

**test \(~\,\) *J liset_name [ time-ini  time-end ] \(~\,\) ...

Each contour desired should be entered as a separate *J command.

Adding the two optional real values time-ini and time-end will cause the \(J\) integral to be evaluated as the \(\Delta J\) integral. Note that this is not an incremental version of \(J\) as the LEFM \(\Delta K\) is used, but rather an evaluation of \(J\) over a path with residual stresses.

Because the \(J\) integral is computed along a boundary, it is using extrapolated Gauss point data to the nodes, which is then again re-interpolated to the intermediate points on the line. This can accumulate some error, especially if the mesh is too coarse. One should verify the stability of \(J\) calculations with respect to path (path independence), and the mesh size.

Also, because this is a ***output option, it is subject to the **frequency command. As the \(J\) integral is integrated over time, for non-linear problems it’s calculation requires a sufficient number of time steps.

Example

***output
 **contour
 **test
  *J path1
  *J path2

***output
 **contour
 **test
  *J path1 0.  10.
  *J path1 20. 30.