An alternative method for indentation of an elastic thin beam by a rigid indenter

Abstract

An alternative method is proposed to solve the problem of a finite-length elastic thin beam indented by a rigid cylindrical indenter. Different from all existing methods, the present method is based on a Kerr-type model that offers a simple differential relation between the applied pressure and the normal deflection of the pressured surface of elastic beam, which holds both inside and outside the contact zone. The width of contact zone, the pressure distribution in contact zone, the deflection outside the contact zone and the load-displacement relation are obtained in explicit form and illustrated with numerical examples. It is confirmed that the indenter loses contact with the beam in the center and the contact zone becomes two separate symmetric strips when the half width of contact-zone becomes large (for example, about four times the beam thickness). In this case, for given beam length and radius of indenter, the present model predicts that the ratio of the contact strip width to the beam thickness is nearly a constant independent of indentation load and beam boundary conditions, and the contact pressure distribution normalized by the average indentation pressure is also nearly independent of indentation load and beam boundary conditions. Efficiency of the present method is demonstrated by comparing its predictions with known basic results available in literature, and the results given by the present method beyond the existing literature are highlighted.