  An indentation experiment involves five variables: indenter shape, material
behavior of the substrate, contact size, applied load and indentation depth.
Only three variable are known afterwards, namely, indenter shape, plus load and
depth as function of time. As the contact size is not measured and the
determination of the material properties is the very aim of the test; two
equations are needed to obtain a mathematically solvable system.
  For elastic materials, the contact size can always be eliminated once and for
all in favor of the depth; a single relation between load, depth and material
properties remains with the latter variable as unknown.
  For viscoelastic materials where hereditary integrals model the constitutive
behavior, the relation between depth and contact size usually depends also on
the (time-dependent) properties of the material. Solving the inverse problem,
i.e., determining the material properties from the experimental data, therefore
needs both equations. Extending Sneddon's analysis of the indentation problem
for elastic materials to include viscoelastic materials, the two equations
mentioned above are derived. To find the time dependence of the material
properties the feasibility of Golden and Graham's method of decomposing
hereditary integrals (J.M. Golden and G.A.C. Graham. Boundary value problems in
linear viscoelasticity, Springer, 1988) is investigated and applied to a single
load-unload process and to sinusoidally driven stationary state indentation
processes.
