2. 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 \(\mathit{dmax}\) around the crack. \(\mathit{dmax}\) is a parameter of the ABSC_CURV_MAXI operator. In the case of a meshed crack ABSC_CURV_MAXI is optional. If \(\mathit{dmax}\) 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 \(\mathrm{\theta }=+\mathrm{\pi }\) and \(\mathrm{\theta }=-\mathrm{\pi }\),

  5. Calculate the difference of the displacement value,

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