A comprehensive review is given of the origins of asymptotic procedures in stress analysis. Specifically, attention is focused on the use of fracture mechanics to characterize the elastic stress state ahead of a crack tip. Analogies are then drawn between this configuration and the stress state adjacent to the apex of a sharp V-notch. Extensions of these asymptotic procedures to bonded and slipping contacts are then considered and it is shown that although power order singularities may be obtained, the solutions are more complicated. Lastly, the use of nested asymptotic procedures are considered in order to account for a small but finite radius at the tip of cracks and notches or at the edge of slipping contacts.
- Asymptotic analysis