Frictionless indentation by a rigid wedge: The effect of tangential displacements in the contact zone

Recent dynamic analyses of frictionless rigid indentation on linearly elastic half-planes assume that the tangential displacement of half-plane points in contact with the indentor is negligible. This assumption is used as a justification for denning the contact zone size, although not known in advance, on the undeformed half-plane, and for uncoupling the tangential and normal displacements in the contact zone. This article examines the validity of this assumption for the symmetric wedge with a constant indentation speed and a contact zone which, as denned on the undeformed half-plane, extends at a constant subcritical rate. Both the coupled and uncoupled solutions are obtained analytically and compared. The difference between the half-plane size defined on the undeformed half-plane and its size on the deformed half-plane may actually be greater for the uncoupled solution. Moreover, the coupled solution does not exhibit the wedge apex stress singularities found for the uncoupled solution.