Indentation Problems

  • J. R. BarberEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 250)


If an elastic–plastic material is indented by a rigid quadratic indenter such as a sphere, the contact problem will exhibit an elastic range, in which the stress field and the force–displacement relation are defined by the Hertzian analysis. The maximum shear stress associated with the axisymmetric Hertzian problem occurs at a depth of 0.48a, where a is the radius of the contact circle and this point reaches both the Tresca and von Mises yield conditions when \(P=P_Y=\frac{21.2S_{Y}^{3}R^{2}}{E^{*}\,^2},\) where \(S_Y\) is the yield stress in uniaxial tension (Johnson in Contact Mechanics, Cambridge University Press, Cambridge, 1985, Johnson 1985).

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA

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