Shot peening is a method widely used in industry to improve fatigue properties of components such as gears. The prediction of stress generation and evolution subsequent to shot peening is important for building reliable lifing models.
The figure below shows a profile of the in plane stress S ||(markers) due to a given distribution of in plane eigenstrain e|| (solid line) introduced into a plate of unit thickness, e.g. by shot peening.
Reference
A.M. Korsunsky, An analysis of residual stresses and strains in shot peening,
in T. Ericsson, Ed., Proc. 5th Intl. Conf. on Residual Stresses (ICRS-5),
Linkoping, Sweden, 16-18 June, 1997.