Abstract
A method is developed for characterising the nature of the plastic zone which develops along the boundary of any notionally complete frictionless contact but where, in practice, there is some small rounding. The approach consists of an outer asymptote, the solution for a semi-infinite square ended rigid punch, whose validity sets the upper limit to the load, and a nested inner asymptote, the solution for a semi-infinite rounded punch, which sets the lower limit to the load. The technique is applied, as an example, to a circular punch, and explicit values of the load given to ensure that the singular field characterises the local stress field to within a given degree of accuracy.
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