Contact between an axisymmetric indenter and a viscoelastic half-space

Lee & Radok introduced a simple method of solving viscoelastic contact problems by replacing the elastic modulus by the viscoelastic creep function, (Lee EH, Radok JRM. Journal of Applied Mechanics 1960;27:438–44) but explained why it fails when the contact area decreases. Tingʹs discovery (Ting TCT. Journal of Applied Mechanics 1966;35:845–54) of the essential mechanism governing unloading of a contact between a sphere and a viscoelastic half-space is used here to develop a relatively simple method of analysis by superposition of an assembly of viscoelastic “Boussinesq” punch indentations. The new method leads to a more convenient form for the variation of the approach during unloading, and this is evaluated for a three-element solid. The same method, with only minor modifications, is then used to evaluate indentation by a conical indenter.