Implementation of extrapolation method
======================================

The extrapolation displacement method is implemented in the POST_T_Q operator which starts by computing the displacement field on the global structure. Since the definition of T-stress are onlyasymptotically true; extrapolation is restricted to the vicinity of the crack tip limited by a maximum distance :math:`\mathit{dmax}` around the crack. :math:`\mathit{dmax}` is a parameter of the ABSC_CURV_MAXI operator. In the case of a meshed crack ABSC_CURV_MAXI is optional. If :math:`\mathit{dmax}` is not defined in the.comm file, by default it is automatically assigned in POST_T_Q operator as equal to three times the maximum size of the mesh elements connected to the nodes on the crack front. The general principle of T-stress computation is defined as follows:


1. Loop on the Crack Tip Nodes


2. Extract the crack tip displacement,


3. Define the plane normal to crack and the crack tip,


4. Project the Displacement Field in :math:`\mathrm{\theta }=+\mathrm{\pi }` and :math:`\mathrm{\theta }=-\mathrm{\pi }`,


5. Calculate the difference of the displacement value,


6. The displacement difference is dividedby :math:`r` with material multiplicative factor will get and then extrapolate into :math:`r=0`. If the solution is perfect, one should get a line. Actually, we get almost a line with a mesh of the "Barsoum" type.