That is, to give local stress components with infinite values in response to any non-zero loading. Such singular stresses typically do reflect the physically high stresses that occur in reality, and accordingly serve to identify locations of potential failure. However, they are useless in themselves for making comparisons with material strength values to determine load levels when failure actually occurs. Examples include the classical crack, keyways in shafts, piston rings on cylinder walls, adhesive butt joints, and so on. For cracks, the associated stress analysis is currently accurately done for the most part, and companion testing carefully performed and furnishing reproducible results.
Predictions made with fracture mechanics are usually trendwise correct.
However, their precision can leave a lot to be desired. Furthermore, extension of fracture mechanics to singular configurations involving other than cracks faces some serious conceptual difficulties. Needed is a new approach if we are ultimately to deal with these pesky stress singularities in a truly reliable way. The approach initiated here is that of improving modeling so that there are no stress singularities. At the outset, the removal of these singularities must be undertaken in the elastic regime because, physically, elastic response precedes plastics.