Improved WCTSE method for the generation of 2D weight functions through implementation into a commercial finite element code

• The complex variable finite element method (ZFEM) was integrated into the Abaqus code.
• The new WCTSE method for 2D weight functions was computed with Abaqus.
• The reference K solution was computed accurately using ZFEM.
• An example weight function was computed and demonstrated to be highly accurate.

The WCTSE (Weight function Complex Taylor Series Expansion) method was recently proposed as a new method for generating 2D weight functions. WCTSE uses a complex variable finite element formulation (ZFEM) to directly compute the derivative of the crack opening displacement with respect to crack length needed for 2D weight functions. The original WCTSE method is further refined in this manuscript through two significant advancements: (1) the methodology has been implemented in the Abaqus commercial finite element program through the use of a user element, and (2) the complex Taylor series expansion method is also used to compute the energy release rate directly from the complex variable finite element analysis; therefore, an independent reference solution for the stress intensity factor is not required. The mode I weight function for a through crack approaching a hole is computed using Abaqus and verified against explicit J-integral results. The results are shown to be very accurate.