Solution of half-plane contact problems by distributing climb dislocations

We derive a novel method for addressing half-plane contact problems by using distributions of climb dislocations over the contact patch to balance the relative overlapping profile of the contacting bodies. Using this technique, we are able to forgo inverting a singular integral equation, simplifying the analysis. We illustrate the method by deriving the associated contact pressures, external forces and applied moments for several examples of both symmetric and non-symmetric indenters.