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We study analytically and numerically the process of indentation ofcylindrical rigid indenter with concave face in form of a power-law function.In the well-known case of a parabolic concave indenter, the contact starts atsharp edges of the indenter and spreads inwards with increasing indentationdepth. For all profiles with the exponent larger than 2, the contact area firstspreads from the boarder inwards, but then a contact is established in thecenter of the indenter. Finally, the outer ring spreads inwards and the centralcontact area outwards until the complete contact is achieved. The criticalindentation depth for the full contact is calculated ones proceeding from thefull contact and looking for the condition of vanishing pressure and alsoproceeding from incomplete contact (in this case numerically, using BoundaryElement Method). The results of both approaches coincide.

Indentation of concave power law profiles with arbitrary exponents