The above-mentioned methods for calculating energy release rate asymptotically approach the actual solution with increased discretization but fail to fully capture the crack tip singularity. More accurate simulations can be performed by utilizing quarter-point elements around the crack tip. These elements have a built-in singularity which more accurately produces stress fields around the crack tip. The advantage of the quarter-point method is that it allows for coarser finite element meshes and greatly reduces computational cost. Furthermore, these elements are derived from small modifications to common finite elements without requiring special computational programs for analysis. For the purposes of this section elastic materials will be examined, although this method can be extended to elastic- plastic fracture mechanics. Assuming perfect elasticity the stress fields will experience a 1 r crack tip singularity.