The elastic field for spherical hertzian contact of isotropic bodies revisited: Some alternative expressions

Closed-form expressions in terms of elementary functionsare derived for the elastic field resulting from spherical Hertzcontact of isotropic bodies. Shear traction is also included usinga Coulomb friction law; thus the shear stress in the contact region is equal to the contact pressure multiplied by a friction coefficient. This paper provides alternative expressions to those recently given by Hamilton (1983) and Sackfield and Hills (1983a). Two methods are outlined for obtaining the present solution and the complete solution for displacements and stresses are given for both normal and tangential loading in terms of just two distortedlength parameters. The elastic field is written in a complex notation allowing the expressions to be put in a compact form. This also allows the expressions for sliding in two directions to be written as simply as for sliding in one direction.