Collapsed 27 node Lagrangian element for three-dimensional stress intensity computations

Considered are the details of a collapsed 27 node (singular) Lagrangian ele ment for use in three-dimensional stress intensity factor calculations. The element is shown to capture both the 1/root r singularity near the front a s required for linear elastic fracture mechanics and a 1/r singularity unde r a relaxed constraint for plastic fracture. It is shown that the radial an d circumferential strains exhibit the singularity, but that direct strain a long the front is zero, thus providing plane strain conditions. Of equal re levance is the quality of mesh at the front. For this we adopt a standard s uite of elements comprising a number of singular 'wedge-shaped' elements ar ound the crack tip in the form of a tube, with the major axis placed along the front. A number of three-dimensional fracture problems are analysed to demonstrate the accuracy and efficiency of the collapsed element, even when used with moderate mesh sizes. (C) 1999 Elsevier Science Ltd. All rights r eserved.