On the detachment of an elastic body bonded to a rigid support (Q1197555)

The problem of an elastic half-space attached to a plane rigid punch over an elliptical region is considered for the case of a centric tension loading \(N\) of the punch. If \(N\) reaches a critical value, detachment occurs. For simplicity it is assumed that (1) the new regions of adhesion are again elliptic and (2) the contact is smooth, i.e. contact shear stresses are absent (the assumption (2), however, can be realized only in the frictionless case of pressure loading, whereas tension loading produces always contact shear stresses in addition to the contact tension stresses, due to the continuity of the displacements and the different materials of the contacting bodies). Based on energy considerations for a prescribed force \(N\) and (alternatively) for a prescribed displacement of the punch \(\Delta\), closed formulae for their critical values are evaluated and it is proved that the detachment starts always at the major half-axis of the elliptic contact region, the equilibrium being unstable.