The singular stress field at the vicinity of the apex of an elastic plane indenter of various angles compressing an elastic half plane was studied by using a complex variable technique. Three particular cases where the indenter is perfectly bonded, slips or adheres according to the Coulomb’s law of friction, to the half plane were considered. The characteristic equations for the determination of the order of the stress singularity at the vicinity of the apex of the indenter for the above three cases were defined in terms of the angle of the indenter and the two composite material parameters α and β first introduced by Dundurs, depicting the mechanical properties of the two materials. The order of singularity at the vertex of the indenter was determined for all material combinations of the indenter and the half plane. Valuable and interesting results were derived.

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