Stability of collapsed 8-node 2-D and 20-node 3-D isoparametric finite elements

The collapse of ordinary finite elements to generate the desired strain singularity at the crack tip for fracture mechanics applications can lead to unwanted additional singularities in that area. Although neither the quarter-point nor the half-point 8-node two-dimensional (2-D) and 20-node three-dimensional (3-D) elements exhibit this behaviour, the present article proves that arbitrarily small deviations from the quarter-point element can be constructed which do have additional singularities. Since the general behaviour of the half-point element is not affected by small modifications, this element is better suited to match complex body geometries.