Generalized Crack Closure Analysis for Elements with Arbitrarily-Placed Side Nodes and Consistent Nodal Forces

A new approach was developed for the evaluation of energy release rate by the virtual crack closure technique in quadratic and linear elements. The generalized method allows arbitrary placement of the side nodes for quadratic elements and thus includes both standard elements, with mid-side nodes, and singularity elements, with quarter-point nodes, as special cases of one general equation. It also accounts for tractionloaded cracks. The new derivation revealed that the proper nodal forces needed for crack closure calculations should be the newly-defined “nodal edge forces,” rather than the global or element forces from standard finite element analysis results. A method is derived for calculating nodal edge forces from global forces. These new forces affect energy release rate calculations for singularity elements and for problems with traction-loaded cracks. Several sample calculations show that the new approach gives improved accuracy.